21. Hecke Operator - Wikipedia, The Free Encyclopedia Algebras of hecke operators are called hecke algebras, a paper on the specialcusp form of Ramanujan, ahead of the general theory given by erich hecke. http://en.wikipedia.org/wiki/Hecke_algebra

Wikimedia needs your help in its 21-day fund drive. See our fundraising page Over US$155,000 has been donated since the drive began on 19 August. Thank you for your generosity! Hecke operator From Wikipedia, the free encyclopedia. (Redirected from Hecke algebra In mathematics , in particular in the theory of modular forms , a Hecke operator is a certain kind of 'averaging' operator that plays a significant role in the structure of vector spaces of modular forms (and more general automorphic representations ). These operators can be realised in a number of contexts; the simplest meaning is combinatorial, namely as taking for a given integer n some function f (Λ) defined on lattices to f with the sum taken over all the Λ′ that are subgroups of Λ of index n . For example, with n =2 and two dimensions, there are three such Λ′. Modular forms are particular kinds of functions of a lattice, subject to conditions making them analytic functions and homogeneous with respect to enlargement of a lattice; these conditions are preserved by the summation and so Hecke operators take modular forms to modular forms. Algebras of Hecke operators are called Hecke algebras , and the most significant basic fact of the theory is that these are commutative rings The theory of Hecke operators on modular forms is often said to have been founded by Mordell in a paper on the special cusp form of Ramanujan , ahead of the general theory given by Erich Hecke . The idea may be considered to go back to earlier work of Hurwitz , who treated correspondences between

22. BibScout - Hecke, Erich Werke / erich hecke. - Goettingen Vandenhoeck Ruprecht, 1959 Bibliotheken http://titan.bsz-bw.de/bibscout/SA-SP/SF1000-SF9900/SF3460-SF4180/SF.3760

@import url(http://titan.bsz-bw.de/bibscout/ploneColumns.css); @import url(http://titan.bsz-bw.de/bibscout/plone.css); @import url(http://titan.bsz-bw.de/bibscout/ploneCustom.css); Skip to content. BibScout web bibscout Home Mathematik Gesammelte Werke Autoren H Hecke, Erich BibScout Home Allgemeines Arch¤ologie Biologie ... Autoren O Hecke, Erich Document Actions Regensburger Verbundklassifikation SF.3760 SF 3760 Mathematische Werke Bibliotheken Mathematische Werke Bibliotheken Mathematische Werke Bibliotheken Erstellt von: BibScout t¤glich aktualisiert Verbund Bayern Thema Hecke, Erich Schlagworte Seite drucken Seitenanfang

23. Math Lessons - Erich Hecke Math Lessons erich hecke. erich hecke. erich hecke (September 20, 1887 –February 13, 1947) was a German mathematician. http://www.mathdaily.com/lessons/Erich_Hecke

Search Mathematics Encyclopedia and Lessons Lessons Popular Subjects algebra arithmetic calculus equations ... more References applied mathematics mathematical games mathematicians more Erich Hecke Erich Hecke September 20 February 13 ) was a German mathematician . He devoted most of his research to the theory of modular forms , creating the general theory of cusp forms holomorphic , for GL (2)), as it is now understood in the classical setting. His early work included establishing the functional equation for the Dedekind zeta function , with a proof based on theta functions . The method extended to the L-functions associated to a class of characters now known as Hecke characters or idele class characters : such L-functions are now known as Hecke L-functions . He was born in Buk Posen Germany (now Poznan Poland ), and died in Copenhagen Denmark See also: Hecke operator , Tate's thesis . External link Last updated: 09-01-2005 14:55:08 algebra arithmetic calculus equations ... mathematicians

24. Julius G. Baron, George Pólya, Wolfgang Pauli, And Erich Hecke Baron, Polya, Pauli, hecke. Circa late 1930s, possibly Zürich. II at StanfordUniversity; Wolfgang Pauli; and erich hecke, a Germanborn mathematician. http://www.aip.org/history/newsletter/spring2001/pic_pauli.htm

Volume XXXIII , No. 1, Spring 2001 RETURN to Spring 2001 Newsletter Photos and Quotes Page RETURN to Spring 2001 Newsletter Table of Contents Center for History of Physics Email: chp@aip.org Phone: 301-209-3165 American Institute of Physics , One Physics Ellipse, College Park, MD 20740-3843. Email: aipinfo@aip.org Phone: 301-209-3100; Fax: 301-209-0843

25. Photos & Quotes: Spring 2001 Newsletter Of The AIP Center For History Of Physics Baron, Polya, Pauli, hecke Circa late 1930s, possibly Zürich. II at StanfordUniversity; Wolfgang Pauli; and erich hecke, a Germanborn mathematician. http://www.aip.org/history/newsletter/spring2001/photospring2001.htm

Photos and Quotes included in the Spring 2001 Issue of the CHP Newsletter Click directly on the photo to see a larger image The U.S. science funding system ca. 1950. A worthy scientist receives a sack of "Ye Swag" from the Renaissance princes of the Office of Naval Research. Drawing by Mike Dormer, reprinted with permission from National Research Council, Ocean Studies Board, Fifty Years of Ocean Discovery: National Science Foundation 1950-2000 The journey back in time reverses the pattern of increasing specialization in science. The high ground of historical perspective helps one to avoid the tunnel vision of the specialist in much the same way that a multidisciplinary approach can foster insight. Edward W. Cliver and Ruth P. Liebowitz Enrico Fermi (1901-1954), on a boat, Isola d'Elba, 1954. Enrico Fermi (1901-1954), circa 1923. Credit: Amaldi Archives, Dipartimento di Fisica, Università "la Sapienza" Rome. Instead of marching onward with perfect vision, science stumbles along... In hindsight, the path taken may look straight, running from ignorance to profound insight, but only because our memory for dead ends is so much worse than that of a rat in a maze.

26. On A Generalization Of A Theorem Of Erich Hecke -- Lee And Weintraub 79 (24): 79 On a Generalization of a Theorem of erich hecke. Ronnie Lee and Steven H. Weintraub.E. hecke initiated the application of representation theory to the http://www.pnas.org/cgi/content/abstract/79/24/7955

This Article Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Alert me to new issues of the journal Add to My File Cabinet Download to citation manager PubMed Articles by Lee, R. Articles by Weintraub, S. H. December 15, 1982 On a Generalization of a Theorem of Erich Hecke Ronnie Lee and Steven H. Weintraub E. Hecke initiated the application of representation theory to the study of cusp forms. He showed that, for p a prime congruent to 3 mod 4, the difference of multiplicities of certain conjugate representations of SL (F p ) on cusp forms of degree 1, level p, and weight (F p ) on certain spaces of cusp forms of degree 2 and level p at parabolic elements of this group. Our results imply that here too, the difference in multiplicities of conjugate representations of Sp (F p ) is a multiple of h(-p). Current Issue Archives Online Submission Info for Authors ... Site Map

27. Bibliography Translate this page hecke, erich, 1887-1947, Mathematische Werke / hrsg. im Auftrage der Akademie der hecke, erich, 1887-1947, Matematische Werke / erich hecke http://www.library.cornell.edu/math/bibliography/display.cgi?start=H&

28. Harald Bohr Correspondence hecke, erich, 192037, 7, German. Heckscher, Eli, 1927-50, 13, Danish The letters from Harald Bohr to erich hecke They were located at the the http://www.math.ku.dk/ths/bohr_h/corresp.htm

Harald Bohr correspondence The destiny of Harald Bohr's correspondence List of major correspondents (more than 1 letter) List of minor correspondents The destiny of Harald Bohr's correspondence The few letters in the Harald Bohr Papers in Copenhagen is a very tiny fraction of the large amount of letters to and from Bohr which once existed. According to Bohr's son, Ole Bohr, Bohr kept the letters he received and organized them well until April 1940 where he destroyed most of them shortly after the German invasion of Denmark. He did that because he was anxious that the Germans should seize on his correspondence and misuse its information about German mathematicians, whom Bohr had helped to leave Germany. According to Asger Aaboe (Yale University), who has had contact with the surviving relatives, the left over of Bohr's collection of correspondence (among other things his correspondence with Godfrey H. Hardy) was kept by Bohr's wife Ulla Bohr for many years, but destroyed by her in the 1970s. There is probably no more correspondence kept by the surviving relatives, at least not any scientific correspondence, and the only part of Bohr's own collection of correspondence which has survived are the letters in the Harald Bohr Papers and some family correspondence (mainly letters to and from his brother Niels) kept in the Family correspondence at the Niels Bohr Archive Hence, the major part of the correspondence listed below is located in other collections. The correspondents are divided in two groups. The first group, which is given alphabetical in a table with links to more details, consists of correspondents where more than one letter to or from Bohr has been conserved. The second group consists of all the minor correspondents where only one letter to or from Bohr has been conserved.

29. Archival Material Related To Jakob Nielsen hecke, erich, 192140, 11, E. hecke Nachlass, Math. Seminar Hamburg. Heegaard, Poul,1935-47, 5, Box 9, Jakob Nielsen Papers. http://www.math.ku.dk/ths/nielsen_j/archival.htm

Archival material related to Jakob Nielsen Jakob Nielsen papers Jakob Nielsen manuscripts Jakob Nielsen correspondence Jakob Nielsen papers A collection of Jakob Nielsen papers is located in the Archive , Institute for Mathematical Science, University of Copenhagen. An inventory of the papers is accessible in Danish and English at the homepages of the Archive. The Nielsen papers are a collection of mathematical reprints, which Nielsen received during his career from various mathematicians. In some cases there are also press clippings related to a person (mainly the Danish mathematicians) or correspondence (see below ). There may also be manuscripts (see below) , but mainly manuscripts by others than Nielsen. Archive no. 6036 at The National Archives, Copenhagen is material from Nielsen from the period 1945-57. There are 3 boxes deposited in 1982. They are inaccessible after the 50 years rule (application needed to get access) and have not been registered. The content is: correspondence, summary of meetings etc. from Nielsen's activities at UNESCO. Jakob Nielsen manuscripts The following manuscripts written by Nielsen are in the Jakob Nielsen papers (box numbers refer to that collection).

30. On A Generalization Of A Theorem Of Erich Hecke On a generalization of a theorem of erich hecke. Ronnie Lee† and Steven H.Weintraub‡. †Department of Mathematics, Yale University, New Haven, http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=347472

31. Proceedings Of The American Mathematical Society hecke, erich. 1938. Lectures on Dirichlet series, modular functions and quadraticforms. Ann Arbor Edwards Brothers. 4. Knopp, Marvin. 1978. http://www.ams.org/proc/2000-128-02/S0002-9939-99-05298-3/home.html

Journals Home Search Author Info Subscribe ... Help ISSN 1088-6826 (e) ISSN 0002-9939 (p) Previous issue Table of contents Next issue Articles in press ... All issues Log-polynomial period functions for nondiscrete Hecke groups Author(s): Abdulkadir Hassen Journal: Proc. Amer. Math. Soc. MSC (1991): Primary 11F66 Posted: July 6, 1999 Retrieve article in: PDF DVI TeX PostScript ... Additional information Abstract: Existence of automorphic integrals associated with nondiscrete Hecke groups will be considered. Multiplier systems for some of these groups will be discussed. References: Evans, Ronald. 1973. A Fundamental Region for Hecke's Modular Groups. J. of Number Theory MR Hassen, Abdulkadir, 1997. Log-Polynomial Period Functions for Hecke Groups. The Ranamujan Journal. To appear. Hecke, Erich. 1938. Lectures on Dirichlet series, modular functions and quadratic forms. Ann Arbor: Edwards Brothers. Knopp, Marvin. 1978.

32. Mathematics Of Computation H erich hecke, Lectures on the theory of algebraic numbers, SpringerVerlag,New York, 1981. MR 83m12001. L AF Lavrik, On functional equations of http://www.ams.org/mcom/2004-73-247/S0025-5718-03-01586-2/home.html

Journals Home Search Author Info Subscribe ... Help ISSN 1088-6842(e) ISSN 0025-5718(p) Previous issue Table of contents Next issue Articles in press ... All issues Stark's conjecture over complex cubic number fields Author(s): David S. Dummit; Brett A. Tangedal; Paul B. van Wamelen. Journal: Math. Comp. MSC (2000): Primary 11R42; Secondary 11Y40, 11R37, 11R16 Posted: August 26, 2003 Retrieve article in: PDF DVI TeX PostScript ... Additional information Abstract: Systematic computation of Stark units over nontotally real base fields is carried out for the first time. Since the information provided by Stark's conjecture is significantly less in this situation than the information provided over totally real base fields, new techniques are required. Precomputing Stark units in relative quadratic extensions (where the conjecture is already known to hold) and coupling this information with the Fincke-Pohst algorithm applied to certain quadratic forms leads to a significant reduction in search time for finding Stark units in larger extensions (where the conjecture is still unproven). Stark's conjecture is verified in each case for these Stark units in larger extensions and explicit generating polynomials for abelian extensions over complex cubic base fields, including Hilbert class fields, are obtained from the minimal polynomials of these new Stark units.

33. Fromm, Erich --  Encyclopædia Britannica erich hecke University of St.Andrews, Scotland Biographical sketch of this Germanmathematician known for his contributions in analytic number theory. http://www.britannica.com/eb/article?tocId=9035492

34. Mathematik In Göttingen: Erich Hecke Translate this page erich hecke wurde in Buk bei Posen (jetzt Poznan, Polen) am 20. September 1887geboren. Er studierte von 1905 bis 1910 in Breslau, Berlin und Göttingen. http://www.math.uni-goettingen.de/Personen/Bedeutende_Mathematiker/hecke.html

Mathematische Fakultät Georg-August-Universität Göttingen Updates: letztes: 20.02.2002 jp                                 [ verantwortlich zurück zur Fakultät Universität Erich Hecke Erich Hecke wurde in Buk bei Posen (jetzt Poznan, Polen) am 20. September 1887 geboren. Er studierte von 1905 bis 1910 in Breslau, Berlin und Göttingen. In Berlin studierte er hauptsächlich bei Edmund Landau, der selbst 1909 nach Göttingen kam. Hecke promovierte 1910 bei Hilbert und habilitierte sich 1912. Zwischen 1910 und 1912 war er Assistent bei Hilbert und Klein, nach 1912 Privatdozent bis er 1915 auf eine Professur in Basel berufen wurde. 1918 nahm er einen Ruf nach Göttingen zurück an, aber im darauffolgenden Jahr ging er an die neugegründete Universität in Hamburg. Während des Kriegs erkrankte er an einem Krebsleiden und mußte operiert werden. Um ihm die Strapazen im Nachkriegsdeutschlands zu ersparen, luden ihn seine dänischen Freunde nach Kopenhagen ein, wo er am 13. Februar 1947 starb. Heckes Doktorarbeit und Habilitationsschrift behandeln den sogenannten "Kroneckerschen Jugendtraum". Kronecker hatte die Vorstellung gehabt, daß man die abelschen Erweiterungskörper eines algebraischen Zahlkörpers durch Adjunktion von speziellen Werten gewisser analytischer Funktionen erzeugen könnte. Er starb 1891, bevor er seine Ideen voll ausgearbeitet hatte. Hilbert nahm diese Frage auf; seine Schüler Blumenthal, Fueter und Hecke drängten soweit vorwärts, wie es zu jener Zeit möglich war. Ihre Ergebnisse sind nicht völlig zufriedenstellend, und beinhalten sogar einige gravierende Fehler; jedoch mußten etwa fünfzig Jahre vergehen, bevor die Mathematik den Entwicklungsstand erreicht hatte, damit diese Fragen richtig gestellt und geantwortet werden konnten. Insbesondere soll hier der in Princeton arbeitende G. Shimura erwähnt werden, der in einer langen Reihe von Veröffentlichungen den Kroneckerschen Jugendtraum zum großen Teil realisiert hat.

35. Members Of The School Of Mathematics hecke, erich HLAVATY, Vaclav HUREWICZ, Witold JOHNSON, Marie M. KETCHUM, Pierce W.KLINE, Morris LEVY, Harry MacDUFFEE, Cyrus C. McCOY, Neal H. http://www.math.ias.edu/1933.html

ALBERT, Abraham Adrian BLUMENTHAL, Leonard M. CAMERON, Robert H. CLIFFORD, Alfred H. GÖDEL, Kurt HEDLUND, Gustav A. HULL, Ralph JACOBSON, Nathan JESSEN, Bärge C. LEHMER, Derrick H. LOWAN, Arnold N. MARTIN, Robert S. PETERSON, Thurman S. RUSE, Harold S. SALKOVER, Meyer SCHMEISER, Mabel F. SCHOENBERG, Isaac J. STAFFORD, Anna A. THOMAS, Tracy Y. TODD, John A. TORRANCE, Charles C. van KAMPEN, Egbertus R. VANDERSLICE, John L. WILDER, Raymond L. ZIPPIN, Leo AUMANN, Georg BARBER, Sherburne F. BLUMENTHAL, Leonard M. BRAUER, Richard D. CAMERON, Robert H. CHURCH, Alonzo CLARKSON, James A. CLIFFORD, Alfred H. DOUGLAS, Jesse DuVAL, Patrick HULL, Ralph LEMAÎTRE, Georges LEWIS, Daniel C., Jr. MAGNUS, Wilhelm MARIA, Alfred J. MARTIN, Robert S. MARTIN, William T. MONTGOMERY, Deane MOORE, Charles N. MURRAY, Francis J. MYERS, Sumner B. NATHAN, David S. SAGEN, Oswald K. SCHOENBERG, Isaac J. SHUDEMAN, Conrad L.B. SIEGEL, Carl L. SINCLAIR, Mary Emily STAFFORD, Anna A. VANDERSLICE, John L. WALSH, Joseph L.

36. Members Of The School Of Mathematics Translate this page hecke, erich, 1937-38. HEDLUND, Gustav A. 1933-34, 1938-39, 1953-54. HEGENBARTH,Friedrich, 1974-75. HEIDER, Lester J. 1957-58. HEIERMANN, Volker, 1998-99 http://www.math.ias.edu/hnames.html

HABICHT, Walter R. HABOUSH, William J. HACHTROUDI, Mohsen HAEFELI, Verena HAEFLIGER, André HAESEMEYER, Christian HAFNER, James L. HAHN, Frank J. HAIMO, Deborah T. HAIMO, Franklin HAIN, Richard M. HAINES, Thomas HAKEN, Wolfgang R.G. HAKULINEN, Ville HALÁSZ, Gábor HALE, Mark P., Jr. HALES, Thomas HALL, Marshall HALMOS, Paul R. HALPERN, James D. HALVERSON, Thomas HAMBLETON, Ian HAMILTON, Richard HAMRICK, Gary C. HAMSTROM, Mary E. HAN, Zheng-Chao HANAMURA, Masaki HANDEL, Michael HANF, William P. HANG, Fengbo HANGES, Nicholas W. HANNER, Olof HARADA, Koichiro HARARY, Frank HARDER, Günter HARDT, Robert HARDY, Godfrey H. HARIS, Stephen J. HARISH-CHANDRA, HARNAD, John HARRIS, Bruno HARRIS, Michael H. HARRIS, Morton E. HARRISON, Virginia C. HARROLD, Orville G., Jr. HARTUNG, Paul G. HARVEY, F. Reese HARVEY, William J. HASENJAEGER, Gisbert HASS, Joel HÅSTAD, Johan HATCHER, Allen E. HAUSEL, Támas HAUSMANN, Jean-Claude HAVER, William E. HAWKINS, Thomas W. HE, Zheng-Xu HECHT, Henryk HECKE, Erich HEDLUND, Gustav A. HEGENBARTH, Friedrich HEIDER, Lester J. HEIERMANN, Volker HEINS, Maurice H.

37. Collected Works In Mathematics And Statistics hecke, erich, 18871947, Mathematische Werke, 1, QA 3 H36 1970, Killam. Heesch,Heinrich, 1906-, Gesammelte Abhandlungen, 1, QA 443 H43 1986, Killam http://www.mathstat.dal.ca/~dilcher/collwks.html

Collected Works in Mathematics and Statistics This is a list of Mathematics and Statistics collected works that can be found at Dalhousie University and at other Halifax universities. The vast majority of these works are located in the Killam Library on the Dalhousie campus. A guide to other locations is given at the end of this list. If a title is owned by both Dalhousie and another university, only the Dalhousie site is listed. For all locations, and for full bibliographic details, see the NOVANET library catalogue This list was compiled, and the collection is being enlarged, with the invaluable help of the Bibliography of Collected Works maintained by the Cornell University Mathematics Library. The thumbnail sketches of mathematicians were taken from the MacTutor History of Mathematics Archive at the University of St. Andrews. For correction, comments, or questions, write to Karl Dilcher ( dilcher@mscs.dal.ca You can scroll through this list, or jump to the beginning of the letter: A B C D ... X-Y-Z A [On to B] [Back to Top] N.H. Abel

38. Modular Form -- Facts, Info, And Encyclopedia Article as the automorphic form concept was understood (for one variable); by (Clicklink for more info and facts about erich hecke) erich hecke from about 1925 http://www.absoluteastronomy.com/encyclopedia/m/mo/modular_form.htm

Modular form [Categories: Analytic number theory, Modular forms, Complex analysis] In (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics , a modular form is an (Click link for more info and facts about analytic function) analytic function on the (Click link for more info and facts about upper half plane) upper half plane satisfying a certain kind of (Click link for more info and facts about functional equation) functional equation and growth condition. The theory of modular forms therefore belongs to (Click link for more info and facts about complex analysis) complex analysis but the main importance of the theory has traditionally been in its connections with (Click link for more info and facts about number theory) number theory . Modular forms appear in other areas, such as (Click link for more info and facts about algebraic topology) algebraic topology and (Click link for more info and facts about string theory) string theory Modular form theory is a special case of the more general theory of (Click link for more info and facts about automorphic form) automorphic form s, and therefore can now be seen as just the most concrete part of a rich theory of

39. Langlands Program -- Facts, Info, And Encyclopedia Article (Click link for more info and facts about erich hecke) erich hecke had earlierrelated Dirichlet Lfunctions with (Click link for more info and facts about http://www.absoluteastronomy.com/encyclopedia/l/la/langlands_program.htm

Langlands program [Categories: Conjectures, Representation theory, Number theory] In (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics , the Langlands program is a web of far-reaching and influential (Reasoning that involves the formation of conclusions from incomplete evidence) conjecture s that connect (Click link for more info and facts about number theory) number theory and the (Click link for more info and facts about representation theory) representation theory of certain ((chemistry) two or more atoms bound together as a single unit and forming part of a molecule) groups . It was proposed by (Click link for more info and facts about Robert Langlands) Robert Langlands beginning in 1967. Connection with number theory The starting point of the program may be seen as the (Click link for more info and facts about Artin) Artin reciprocity law which generalizes (Click link for more info and facts about quadratic reciprocity) quadratic reciprocity . Artin's law applies to an (Click link for more info and facts about algebraic number field) algebraic number field whose (Click link for more info and facts about Galois group) Galois group over Q is (Click link for more info and facts about abelian) abelian , assigns (Click link for more info and facts about L-function) L-function s to the one-dimensional representations of this Galois group; and states that these L-functions are identical to certain

40. Abstract For 2002/10/21: Russo In the mid 1930 s, erich hecke clarified the connection by way of the Mellintransform. He established a correspondence theorem between Dirichlet series http://www.math.binghamton.edu/dept/ComboSem/abstract.200210rus.html

Daniel T. Russo Conjugation in the Theory of Hecke Correspondence Abstract for the Combinatorics and Number Theory Seminar 2002 October 21 A Hecke correspondence is an association between entire modular (or automorphic) forms and Dirichlet series satisfying a prescribed functional equation. This association can be traced back to 1859 in a short memoir by Bernhard Riemann where he states the now-famous Riemann Hypothesis. There, he dealt with the Riemann Zeta function, the prototype for Dirichlet series, and the theta function, an entire modular form on the theta group. In the mid 1930's, Erich Hecke clarified the connection by way of the Mellin transform. He established a correspondence theorem between Dirichlet series satisfying a functional equation (and certain analytic conditions) and entire automorphic forms on the Hecke groups.

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