Theory

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• Science: Math: Geometry: Algebraic Geometry  (109)

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• Number Theory Web   - Things of interest to number theorists collected by Keith Matthews.

• 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.
• 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.
• 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).
• An Introduction to the Theory of Numbers by Leo Moser - Textbook covering following topics: compositions and partitions; arithmetic functions; distribution of primes; irrational numbers; congruences; diophantine equations; combinatorial number theory; and geometry of numbers.
• Klein Polyhedra - Examples and algorithms for computing Klein polyhedra, also known as Arnold sails or veils (voiles), by Keith Briggs.
• 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 Algebraic Numbers - 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.
• 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.
• Noncommutative Geometry, Trace Formulae and the Zeroes of the Riemann Zeta Function - Lecture notes by Alain Connes.
• Number Theory - Proofs along with equation solvers and graphical views written in Java.
• Number Theory - Dave Rusin's guide to number theory.
• 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.
• 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.
• 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.
• Transcendental Numbers - Maple worksheets, lecture notes and links to other resources by John Cosgrove.
• 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.
• Vignettes on Automorphic and Modular forms, Representations, L-functions, and Number Theory - By Paul Garrett.
• Visible Structures in Number Theory - By Peter Borwein and Loki Jörgenson. Recognising number patterns visually.
• The Work of Robert Langlands - Thesis, papers, manuscripts, letters and bibliography.
• World Records for Numerical Palindromes - The 196 Palindrome Quest and The Most Delayed Palindromic Number, by Jason Doucette.