1. Number Theory - Wikipedia, The Free Encyclopedia number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider http://en.wikipedia.org/wiki/Number_theory

Number theory From Wikipedia, the free encyclopedia Jump to: navigation search Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. Number theory may be subdivided into several fields, according to the methods used and the type of questions investigated. ( See the list of number theory topics The term " arithmetic " is also used to refer to number theory. This is a somewhat older term, which is no longer as popular as it once was. Number theory used to be called the higher arithmetic , but this too is dropping out of use. Nevertheless, it still shows up in the names of mathematical fields ( arithmetic functions arithmetic of elliptic curves fundamental theorem of arithmetic ). This sense of the term arithmetic should not be confused either with elementary arithmetic , or with the branch of logic which studies Peano arithmetic as a formal system Mathematicians working in the field of number theory are called number theorists When arranging the natural numbers in a spiral and emphasizing the prime numbers, an intriguing and not fully explained pattern is observed, called the

2. NUMBER THEORY WEB Things of interest to number theorists collected by Keith Matthews. http://www.numbertheory.org/

Number Theory Web Aims New Listings Number theorists' Home Pages/Departmental listings Things of Interest to Number Theorists ... Search the Number Theory Web Pages The main site is hosted on computers in downtown Vancouver, as of 31st May 2003, courtesy of ASRAD The Italian The British mirror site is at University of Cambridge, UK The Japanese mirror site is at University of Electro-Communication, Tokyo Created and maintained by Keith Matthews , Brisbane, Australia Suggestions for additions or improvements are welcome. Email: webmaster@numbertheory.org Last modified 13th July 2006

3. 11: Number Theory Dave Rusin s guide to number theory. http://www.math.niu.edu/~rusin/known-math/index/11-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 11: Number theory Introduction Number theory is one of the oldest branches of pure mathematics, and one of the largest. Of course, it concerns questions about numbers, usually meaning whole numbers or rational numbers (fractions). Elementary number theory involves divisibility among integers the division "algorithm", the Euclidean algorithm (and thus the existence of greatest common divisors), elementary properties of primes (the unique factorization theorem, the infinitude of primes), congruences (and the structure of the sets Z /n Z as commutative rings), including Fermat's little theorem and Euler's theorem extending it. But the term "elementary" is usually used in this setting only to mean that no advanced tools from other areas are used not The remaining parts of number theory are more or less closely allied with other branches of mathematics, and typically use tools from those areas. For example, many questions in number theory may be posed as Diophantine equations equations to be solved in integers without much preparation. Catalan's conjecture are 8 and 9 the only consecutive powers? asks for the solution to

4. MathPages: Number Theory Kevin Brown s collection of sci.math postings related to number theory topics. http://www.mathpages.com/home/inumber.htm

Number Theory Symmetric Pseudoprimes Is e Normal? Identities for Linear Recurring Sequences The Half-Totient Tree ... Math Pages Main Menu

5. Number Theory Quadratic two integer variable equation solver, quadratic modular equations, sum of powers. http://www.alpertron.com.ar/NUMBERT.HTM

Dario Alpern's site Home Page Ver sitio en castellano ELECTRONICS Intel Microprocessors (Spanish only) MATHEMATICS Calculators Number Theory Problems PROGRAMS Assembler 80386 (downloads) Java Games CONTACT Personal Comments Guestbook Links ... Donations Number theory This site features: Generic Two integer variable equation solver Diophantine equation ax + bxy + cy + dx + ey + f = solver, where the unknowns x and y can be integer numbers only. Written in Java/JavaScript. Last updated on May 31st, 2001. Quadratic modular equation solver Calculator that can solve equations of the form ax + bx + c = (mod n) . Last updated: May 2nd, 2002. Sum of powers Table of relations of the form a p + b q = c r with gcd(a,b,c) = 1 . Last updated: September 7th, 2003. Ulam's Spiral Java applet featuring a graphical view of prime numbers. Last updated on February 14th, 2003. Factorization using the Elliptic Curve Method Applet that can be used to find 20- or 30-digit factors of numbers or numerical expressions up to 1000 digits long. It also computes the number and sum of divisors, Euler's totient and Moebius, and its decomposition as a sum of up to 4 perfect squares. Last updated on February 9th, 2003. Gaussian Integer Factorization applet Finds the factors of complex numbers of the form a+bi where a and b are integers. It also includes a complete calculator with operators and functions using gaussian integers. Last updated on June 1st, 2002.

6. Front: Math.NT Number Theory Very large number theory section of the mathematics eprint arXiv. http://front.math.ucdavis.edu/math.NT

Front for the arXiv Fri, 14 Mar 2008 Front math NT search register submit journals ... iFAQ math.NT Number Theory Calendar Search Atom feed Search Author Title/ID Abstract+ Category articles per page Show Search help Recent New articles (last 12) 14 Mar arXiv:0803.1891 Partition statistics and quasiweak Maass forms. K. Bringmann , F. Garvan , K. Mahlburg math.NT math.CO 14 Mar arXiv:0803.1870 Non-vanishing of the symmetric square $L$-function at the central point. Rizwanur Khan math.NT 14 Mar arXiv:0803.1868 On the Distribution of Normal Numbers. Rizwanur Khan math.NT 13 Mar arXiv:0803.1740 Hongze Li , Hao Pan math.NT 13 Mar arXiv:0803.1682 An open image theorem for a general class of abelian varieties. Chris Hall math.NT 12 Mar arXiv:0803.1606 Symmetric Numerical Semigroups Generated by Fibonacci and Lucas Triples. Leonid G. Fel math.NT math.AC 12 Mar arXiv:0803.1584 Distribution of Angles in Hyperbolic Lattices. Morten S. Risager , Jimi L. Truelsen math.NT Cross-listings 14 Mar arXiv:0803.1996 Rational points on homogeneous varieties and Equidistribution of Adelic periods. Alex Gorodnik , Hee Oh (with appendix by Mikhail Borovoi).

7. The Math Forum - Math Library - Number Theory The Math Forum s Internet Math Library is a comprehensive catalog of Web sites and Web pages relating to the study of mathematics. This page contains sites http://mathforum.org/library/topics/number_theory/

Browse and Search the Library Home Math Topics : Number Theory Library Home Search Full Table of Contents Suggest a Link ... Library Help Subcategories (see also All Sites in this category Algebraic Number Theory Analytic Number Theory Sequences and Sets Fibonacci Sequence Selected Sites (see also All Sites in this category Continued Fractions: an Introduction - Adam Van Tuyl A brief introduction to the field of continued fractions, including some basic theory about the subject; the history of continued fractions, tracing some of the major developments in the field in the past 2500 years; some interactive applications that demonstrate the uses of continued fractions and let you calculate them; and the resources used in creating this site, including a bibliography and links to other sites on the Web. more>> Fermat's Last Theorem - MacTutor Math History Archives Essay describing Fermat's theorem with links to mathematicians such as Sophie Germain, Legendre, Dirichlet, Shimura and Taniyama, etc., from its inception through Andrew Wiles' proof, with another web site and 17 references (books/articles). more>> Number Theory - Dave Rusin; The Mathematical Atlas

8. Number Theory www.mathgoodies.com/lessons/toc_vol3.shtm http://www.mathgoodies.com/lessons/toc_vol3.shtm

9. Number Theory - Physicsworld.com number theory. A physicist in the US has proposed a new way of quantifying the scientific output of individual scientists. Jorge Hirsch of the University of http://physicsworld.com/cws/article/news/22890

@import url(/cws/css/screen.css); @import url(/cws/css/themes/phw.css); @import url(/cws/css/datePicker.css); Skip to the content A community website from IOP Publishing Sign in Forgotten your password? Sign up physicsworld.com Realmedia.OAS_AD('Top'); Home Print edition Latest issue Index ... Advertising Whole site Print edition News In depth Jobs Events Buyer's guide Search Related Stories Why some papers last longer that others World order upset by new citation study Related Links An index to quantify an individual's scientific output ISI Web of Knowledge Jorge Hirsch homepage Realmedia.OAS_AD('Left'); Key Suppliers More companies Corporate Partners For maximum exposure, become a Corporate Partner. Contact our sales team Corporate Partners News Aug 16, 2005 Number theory A physicist in the US has proposed a new way of quantifying the scientific output of individual scientists. Jorge Hirsch of the University of California at San Diego says that the " h -index" - which is derived from the number of times that papers by the scientist are cited - gives an estimate of the "importance, significance and broad impact of a scientist's cumulative contributions." According to Hirsch the h -index "should provide a useful yardstick to compare different individuals" when recruiting new staff, deciding promotions and awarding grants (physics/0508025).

10. Number Theory Files For David Eppstein I have implemented a number of simple numbertheoretic algorithms Other number theory on the web Recreational topics from the theory of numbers http://www.ics.uci.edu/~eppstein/numth/

Number-Theoretic Hacks I have implemented a number of simple number-theoretic algorithms for my own amusement, and provide them here on the net. Egyptian Fractions algorithms and references. This notebook for Mathematica 2.2/Macintosh (also available in HTML format) describes and implements a number of different algorithms for representing rational numbers as sums of distinct unit fractions. C++ implementation of J.H.Conway's "nimber" arithmetic. Conway's nimbers (used in combinatorial game theory ) form an infinite field of characteristic two, with a natural binary representation in which truncation to a fixed number of bits produces finite subfields GF[2^2^k]. The algorithms in this file implement nimber multiplication, square root, and other functions, using O(k 3^k) bit operations. This bound is somewhat worse than what one can achieve for the more standard irreducible polynomial representation of GF[2^2^k] but is simpler and more uniform. This version is an update to my code by Achim Flammenkamp, to make it run under less archaic versions of C++ and allow numbers with more bits than machine precision; the original code is here C++ fast algorithm for computing 2-adic inverse.

11. Number Theory, Math, Online Tutoring - Tutorvista.com Number and Operations is an essential part of the study of mathematics. A number is a quantity that is used in counting and measuring. http://www.tutorvista.com/content/math/number-theory/number-theory.php

Welcome! Customer Care Chat Login Subject Math > Number Theory Number Theory Number and Operations is an essential part of the study of mathematics. A number is a quantity that is used in counting and measuring. The definition of the term number includes such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers. The study of Number and Operations involves understanding numbers, representations, relationships, and number systems. Operations on numbers produces a new value from one or more input values. Although Operations can involve dissimilar objects and mathematical objects other than numbers, they may not be defined every possible value. Operations use operands, arguments, or inputs, to produce value, result, or output. Rational and Irrational Numbers The rational numbers can be expressed as terminating or recurring decimals. Numbers which are not rational are called irrational numbers. When expressed as decimals, they are non-terminating and non-recurring. We can obtain infinite number of irrationals between two irrational numbers.

12. A Computational Introduction To Number Theory And Algebra By Victor Shoup (Cambridge University Press, 2005). Full text free in PDF, list of errata, supplementary exercises. http://www.shoup.net/ntb/

A Computational Introduction to Number Theory and Algebra A book introducing basic concepts from computational number theory and algebra, including all the necessary mathematical background. The book is published by Cambridge University Press . It can be purchased directly from Cambridge University Press , or from online book retailers . However, the book will continue to be freely available online in PDF format under a Creative Commons license. DOWNLOADS Version 2.2 [ pdf ] (1/21/2008, not yet available in print) Version 1 [ pdf ] (1/15/2005, corresponds to the print edition) List of errata [ pdf Supplementary material [ pdf many additional exercises and examples some alternative proofs and stronger theorems LINKS Review in SIGACT News Vol 37, No 1 Back to Victor Shoup's Home Page

13. NUMBER THEORY WEB (BRITISH MIRROR SITE) Search the number theory Web Pages. The main site is in Vancouver, as of 31st May 2003 The Italian mirror site is at Università di Roma Tre, Rome, Italy http://www.dpmms.cam.ac.uk/Number-Theory-Web/

Number Theory Web (British Mirror Site) Aims New Listings Number theorists' Home Pages/Departmental listings Things of Interest to Number Theorists ... Search the Number Theory Web Pages The main site is in Vancouver, as of 31st May 2003 The Italian mirror site The British mirror site is at University of Cambridge, UK The Japanese mirror site is at University of Electro-Communication, Tokyo Created and maintained by Keith Matthews , Dept of Mathematics, University of Queensland, Brisbane, Australia Suggestions for additions or improvements are welcome. Email: krm@internode.on.net Last modified 16th November 2004

14. Algebraic Number Theory Archives Electronic preprint archives for mathematics research papers in algebraic number theory and arithmetic geometry. http://www.math.uiuc.edu/Algebraic-Number-Theory/

Algebraic Number Theory Archives Date: Wed, 8 Jan 2003 12:03:33 -0600 (CST) To: Algebraic-Number-Theory@listserv.uiuc.edu Subject: Algebraic-Number-Theory preprint archives I shall no longer be managing the Algebraic Number Theory preprint archives. The web site is now frozen and is not accepting new submissions and subscriptions. Michael Zieve has kindly agreed to assume control, with the help of Greg Kuperberg, and new submissions should be directed to the new URL for the archive, http://front.math.ucdavis.edu/ANT/ Your subscription will continue, unless you choose otherwise. I thank Dan Grayson for setting up the archives and his patient help with technical issues, and Michael and Greg for volunteering to take on this work. Nigel Boston http://www.math.wisc.edu/~boston/ Welcome to the preprint archives for papers in Algebraic Number Theory and Arithmetic Geometry. Use the Find facility of your browser on this page, or search: Our mirror site in the United Kingdom , set up by Richard Pinch. Our main site in the USA Instructions for authors Instructions for joining the mailing list . Members of the mailing list receive announcements of preprints when they are deposited in the archives. Some TeX fonts , stored in a tar image compressed with gzip, including the lams* and xy* fonts, which are needed for some of the preprints.

15. Università Degli Studi Di Ferrara - Cerca in rete number theory. Old page Bibliography General General. number theory Web Mirror in Roma Internet resources in number theory http://felix.unife.it/ /ma-zth

LA PAGINA RICERCATA NON ESISTE O E' STATA RIMOSSA. L'indirizzo del portale dell'Università degli Studi di Ferrara è : http://www.unife.it/ Aiuto In Internet unife.it

16. PlanetMath: Number Theory number theory is the branch of math concerned with the study of the integers, and of the objects and structures that naturally arise from their study. http://planetmath.org/encyclopedia/NumberTheory.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... RSS Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About number theory (Topic) Number theory is the branch of math concerned with the study of the integers , and of the objects and structures that naturally arise from their study. It is one of the oldest parts of mathematics, alongside geometry , and has been studied at least since the ancient Mesopotamians. Perhaps because of its purely mathematical nature (at least until the development of cryptography in the twentieth century, number theory was devoid of practical applications), number theory has often been considered as a central and particularly beautiful part of mathematics. Carl Friedrich Gauss , arguably the greatest number Euler , Gauss, Dedekind, Jacobi, Eisenstein and Hilbert all made immense contribution to its development. Great twentieth century number theorists include Artin, Hardy, Ramanujan Andrew Wiles Number theory is also remarkable because small, easy-to-understand

17. Number Theory Authors/titles Recent Submissions Subjects number theory (math.NT); Mathematical Physics (mathph) Comments 12 pages. Subjects Algebraic Geometry (math.AG); number theory (math.NT) http://arxiv.org/list/math.NT/recent

arXiv.org math math.NT Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages Number Theory Authors and titles for recent submissions Fri, 14 Mar 2008 Thu, 13 Mar 2008 Wed, 12 Mar 2008 Tue, 11 Mar 2008 ... Mon, 10 Mar 2008 [ total of 21 entries: [ showing up to 25 entries per page: fewer more Fri, 14 Mar 2008 arXiv:0803.1891 ps pdf other Title: Partition statistics and quasiweak Maass forms Authors: K. Bringmann F. Garvan K. Mahlburg Subjects: Number Theory (math.NT) ; Combinatorics (math.CO) arXiv:0803.1870 ps pdf other Title: Non-vanishing of the symmetric square $L$-function at the central point Authors: Rizwanur Khan Comments: 31 pages Subjects: Number Theory (math.NT) arXiv:0803.1868 ps pdf other Title: On the Distribution of Normal Numbers Authors: Rizwanur Khan Comments: 14 pages Subjects: Number Theory (math.NT) arXiv:0803.1996 (cross-list from math.AG) [ ps pdf other Title: Rational points on homogeneous varieties and Equidistribution of Adelic periods Authors: Alex Gorodnik Hee Oh (with appendix by Mikhail Borovoi) Comments: 58 pages, and 27 pages of appendix

18. ScienceDirect - Journal Of Number Theory, Volume 128, Issue 4, Pages 709-1090 (A Journal of number theory Copyright © 2007 Elsevier Inc. All rights reserved Shortcut URL to this page http//www.sciencedirect.com/science/journal/0022314X http://www.sciencedirect.com/science/journal/0022314X

Athens/Institution Login Not Registered? User Name: Password: Remember me on this computer Forgotten password? Home Browse My Settings ... Help Quick Search Title, abstract, keywords Author e.g. j s smith Journal/book title Volume Issue Page Journal of Number Theory Shortcut URL to this page: http://www.sciencedirect.com/science/journal/0022314X Alert me about new Journal Issues Add to Favorites setCheckedBoxes ('/scidirimg/sci_dir', 'btn_apply1.gif', 'btn_apply1.gif'); Sample Issue Online About this Journal Submit your Article = Full-text available = Non-subscribed What does this mean? Articles in Press Volumes 121 - 128 (2006 - 2008) Volume 128, Issue 4 pp. 709-1090 (April 2008) Volume 128, Issue 3 pp. 453-708 (March 2008) Volume 128, Issue 2 pp. 235-452 (February 2008) Volume 128, Issue 1 pp. 1-234 (January 2008) Volume 127, Issue 2 pp. 145-330 (December 2007) Volume 127, Issue 1 pp. 1-144 (November 2007) Volume 126, Issue 2 pp. 155-296 (October 2007) Volume 126, Issue 1 pp. 1-154 (September 2007) Volume 125, Issue 2

19. Number Theory number theory Group. Members, meetings, software. http://www.ma.utexas.edu/~voloch/numberthy.html

Number Theory at the Mathematics Dept. of the University of Texas Permanent faculty in Number Theory, and their fields of interest. David Helm dhelm@math.utexas.edu ): The arithmetic of Shimura varieties and its application to automorphic forms, Galois representations, and the Langlands program. John Tate tate@math.utexas.edu ): Algebraic Number Theory (local and global fields), Class Field Theory, Galois cohomology, Galois representations, L-functions and their special values, modular forms, elliptic curves and abelian varieties. Jeffrey Vaaler vaaler@math.utexas.edu ): Analytic number theory, Diophantine approximation and the geometry of numbers in local and global fields, Diophantine inequalities, polynomials, effective measures of irrationality and transcendence, applications of Fourier analysis in number theory, inequalities and extremal problems. villegas@math.utexas.edu ): Special values of L-functions (Birch-Swinnerton-Dyer and Bloch-Beilinson conjectures), arithmetic of elliptic curves, modular forms, Mahler measure of polynomials. Felipe Voloch ): Arithmetic of function fields. Diophantine geometry over function fields. Geometry of algebraic curves. Algebraic varieties over finite fields. Modular forms, elliptic curves and abelian varieties. Finite fields and applications to coding theory and cryptography.

20. Journal Of Number Theory - Elsevier The Journal of number theory features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied http://www.elsevier.com/locate/jnt

Home Site map Elsevier websites Alerts ... Journal of Number Theory Journal information Product description Editorial board Audience Abstracting/indexing ... Special issues and supplements Subscription information Bibliographic and ordering information Conditions of sale Dispatch dates Journal-related information Contact the publisher Impact factor Most downloaded articles Other journals in same subject area ... Select your view JOURNAL OF NUMBER THEORY Editor-in-Chief: D. Goss See editorial board for all editors information Description The Journal of Number Theory features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. ISSN: 0022-314X Imprint: ACADEMIC PRESS Subscriptions for the year 2008, Volume 128, 12 issues Institutional online access: ScienceDirect eSelect For purchase of online access to this journal on ScienceDirect. Personal price: Order form EUR 1,493 for European countries and Iran

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