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Algebraic
A Brief Introduction to Classical and Adelic Algeb, Algebraic Number Theory, Algebraic Number Theory, Algebraic Number Theory, Algebraic Number Theory and Automorphic L-function, Binary Cubic Forms and Cubic Number Fields, Class Field Theory, Cyclotomic Fields Virtual Study Group, Discriminant Exponent Calculator, Galois Groups and Greenberg's Conjecture
Analytic
Riemann Hypothesis, A Prime Case of Chaos, A Three-dimensional Model of the zeta Function, Analytic Number Theory, Critical Strip Explorer, Directory of All Known Zeta Functions, Inexplicable Secrets of Creation, Irrationality and Transcendence, Not Always Buried Deep, Riemann's Paper, Riemann's Zeta function
Chats and Forums
Archives of Number Theory List, FermatNumbers, goldbach, numbertheory, PrimeForm, Primenumbers, SeqFan Mailing List, Somos Sequence Mailing List Archive
Computational
Algorithm Design Manual - Number Theoretic Algorit, Algorithmic Number Theory, Basics of Computational Number Theory, Computational Number Theory, Computational Projects in Number Theory, Future Directions in Algorithmic Number Theory, Implementations of Extended LLL, LLL Page, Some Number Records, Suggested Readings in Algorithmic Number Theory
Diophantine Equations
Equal Sums of Like Powers, Fermat's Last Theorem, Bibliography on Hilbert's Tenth Problem, Developing A General 2nd Degree Diophantine Equati, Diagonal Quartic Surfaces, Diophantine Equations, Diophantine Geometry in Characteristic p, Diophantine m-tuples, Diophantus Quadraticus, Egyptian Fractions, Fermat's Method of Infinite Descent, Hilbert's Tenth Problem
Education
A Collection of Lecture Notes, A Self-learning Package in Elementary Number Theor, Course Notes by Jim Milne, Courses and Lecture Notes in Number Theory, Elementary and Algebraic Number Theory, Elementary and Analytic Number Theory, Elementary Number Theory, Elementary Number Theory, Elementary Number Theory -- A Lightning Course, Expositions and Notes
Elliptic Curves and Modular Forms
Software, Tables, 14H52: Elliptic Curves, A Proof of the Full Shimura-Taniyama-Weil Conjectu, Algorithms for Modular Elliptic Curves, An Elementary Introduction to Elliptic Curves, Arithmetic of Cuves, Bibliography for Automorphic and Modular Forms, L-, Counting Points on Elliptic Curves, Course Notes, ECDL Project, ECMNET
Events
Past Events, Series, 17th Czech and Slovak International Conference on , Additive Combinatorics, Algebraic Geometry and Number Theory, Analysis in Number Theory, Analytic Methods for Diophantine Equations, ANTS VII, CANT 2005, Cohomological Approaches to Rational Points, Computational Number Theory and Applications to Cr, Computational Number Theory Workshop
Factoring
Division Rules, Perfect Numbers, Tables, Computing Aurifeuillian factors, Discovery of a Lost Factoring Machine, Factoring Fermat Numbers, Factoring Papers, Factoris, Factorization of F10, Factorization of RSA-155, Factorization Using the Elliptic Curve Method, Factorizations of Near-repdigit Numbers, FactorWorld
History
A Guide to the Emil Grosswald Papers, Euler's Contribution To Number Theory, Fermat's Little Theorem, Historical Essays in Number Theory, Historical Things in Number Theory, History of Arithmetic and Number Theory, Mathematical Manuscripts at Trinity College Cambri
Open Problems
ABC Conjecture, Catalan Conjecture, Collatz Problem, Goldbach Conjecture, Advice to Research Students, L-functions and Random Matrix Theory, Mathematician's Secret Room, Number Theory Conjectures, Open Problems, Seva Lev's Problem Page, Unsolved Problems and Conjectures, Unsolved Problems and Rewards
People
A, B, C, D, E, F, G, H, I, J
Prime Numbers
Mersenne, Primality Tests, A List of Prime Numbers, Aesthetics of the Prime Numbers Sequence, Animation of Eratosthenes' Prime Sieve, Applets for Prime Numbers, Ask Dr. Math, Basic Theorems Concerning Prime Numbers, Bipeds and Prime Numbers, Cunningham Chain Records, Deficient Factorials, Distribution of the Prime Numbers
Publications
Bibliographies, Books, Journals, Preprint Archives, Theses, Basic Library List in Number Theory, Number Theory Books from 1996, Research papers by János A. Csirik
Research Groups
(Austria) Technical University of Graz, (Austria) University of Natural Resources, Vienna, (Austria) University of Vienna, (Brazil) Universidade de Brasília, (Canada) CICMA, Concordia University, Montreal, (Canada) McMaster University, (Canada) McMaster University, (Canada) Simon Fraser University, (Canada) University of British Columbia, (Canada) University of Toronto
Software
Pari-GP, UBASIC, Aliquot, apfloat, ARIBAS, BIG_INT, CALC, CLN - Class Library for Numbers, ECMNET, Encyclopedia of Integer Sequences Seeker, Factorizer, FTP Sites, Calculator Programs and Archives
Tables
Algorithmic Number Theory: Tables and Links, Algorithms for Solving Index Form Equations and Co, Bernoulli Computations, Carmichael and Perrin, Carmichael Numbers and Lehmer's Problem, Cubic Field Extensions, Curves of Genus 2, Database for Polynomials over the Rationals, Database of Local Fields, Dedekind Zeta Functions
A Mechanical Proof of Quadratic Reciprocity
A paper by David M. Russinoff describing the use of the Boyer-Moore theorem prover in mechanically generating a proof of the Law of Quadratic Reciprocity. PS/PDF.
About Two Months of Computing
Work on the 196 palindrome problem by Tim Irvin.
Active Elementary Number Theory
Interactive (Javascript) expression of a number as a sum of two squares.
Application of Digital Root
A test for the terms of a sequence being expressed by a polynomial, by Roupam Ghosh.
Covers, Sumsets and Zero-sums
A unified approach to covering systems, restricted sumsets and zero-sum problems by Zhi-Wei Sun.
Fermat's Little Theorem
With notes on Carmichael numbers and the life of R.D. Carmichael.
Frequently Asked Questions
Number Theory section of the sci.math FAQ list.
Hakmem Continued Fractions
Some notes from the MIT collection. Includes Gosper's algorithms for CF arithmetic.
Infinite Series Theorem
Addresses the question whether a series of rational functions converges to a rational number.
Integer Relations
To determine linear integer dependence among numerical constants and to determine the minimal polynomial of an approximate algebraic number. Interactive or via email.
Introduction to Bernoulli Numbers
A web article with a brief history and account of their relationship with the Riemann zeta function and Fermat's Last Theorem (HTML/PS).
Klein Polyhedra
Examples and algorithms for computing Klein polyhedra, also known as Arnold sails or veils (voiles), by Keith Briggs.
L-Functions
Classified by degree, then by level, then by eigenvalue, then by root number.
Lehmer's Conjecture
That the Mahler measure of an algebraic number is bounded away from 1. Pages by Michael Mossinghoff, UCLA.
Linear Independence Measures for Logarithms of Alg
Michel Waldschmidt. Cetraro summer school lectures, July 2000.
MathPages: Number Theory
Kevin Brown's collection of sci.math postings related to number theory topics.
MathWorld Number Theory
Index to articles in Eric Weisstein's MathWorld in the area of number theory.
Noncommutative Geometry, Trace Formulae and the Ze
Lecture notes by Alain Connes.
Number Theory
Dave Rusin's guide to number theory.
Number Theory
Proofs along with equation solvers and graphical views written in Java.
Number Theory Foundation
Aims to collect donations from supporters of number theory and to disburse these donations to encourage research.
Number Theory Glossary
Compiled by Robert Campbell.
Number Theory Web
Things of interest to number theorists collected by Keith Matthews.
On-Line Encyclopedia of Integer Sequences
Given an integer sequence, find its name, and formula.
Online Seminar: Galois theory of p-Extensions
Email seminar on "Galoissche Theorie der p-Erweiterungen" by Helmut Koch.
Other Maths
A wide selection of number theory topics compiled by Jon Perry.
Some Highlights of Arithmetic Combinatorics
Lecture notes and resources on combinatorial number theory by Terence Tao.
Some Number-Theoretical Constants
Products of rational functions of p over primes, computed by Gerhard Niklasch and Pieter Moree.
Somos Polynomials
Related to Somos sequences and elliptic theta functions.
Square-free Gaps
Algorithm and source code for the calculation of square-free numbers and gaps.
The Arithmetic Properties of Binomial Coefficients
Activated text by Andrew Granville.
The Canadian Number Theory Association
A loosely defined group of individuals, mainly in Canada, active in research in Number Theory.
The Somos Sequence Site
Web resources for information on Somos sequences and related topics such as elliptic divisibility sequences.
The Valuation Theory Home Page
A forum for all mathematicians who work in valuation theory or apply valuation theoretical results in their own field of research.
The Work of Robert Langlands
Thesis, papers, manuscripts, letters and bibliography.
Three Years of Computing
Palindrome Quest. Reporting computations on the 196 problem.
Transcendental Numbers
Maple worksheets, lecture notes and links to other resources by John Cosgrove.
Vignettes on Automorphic and Modular forms, Repres
By Paul Garrett.
Visible Structures in Number Theory
By Peter Borwein and Loki Jörgenson. Recognising number patterns visually.
World Records for Numerical Palindromes
The 196 Palindrome Quest and The Most Delayed Palindromic Number, by Jason Doucette.