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Science: Math: Number_Theory


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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).

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.

L-Functions
Classified by degree, then by level, then by eigenvalue, then by root number.

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.

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.

The Somos Sequence Site
Web resources for information on Somos sequences and related topics such as elliptic divisibility sequences.

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 J├Ârgenson. 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.

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