Logic and Foundations

Noncommutative Geometry, Trace Formulae and the Zeroes of the Riemann Zeta Function Noncommutative Geometry, Trace Formulae and the Zeroes of the Riemann Zeta Function- Lecture notes by Alain Connes. LMFDB LMFDB- A handbook including tables, formulas, links, and references for L-functions and the underlying objects. Transcendental Numbers Transcendental Numbers- Maple worksheets, lecture notes and links to other resources by John Cosgrove. Visible Structures in Number Theory Visible Structures in Number Theory- By Peter Borwein and Loki Jörgenson. Recognising number patterns visually. Some Number-Theoretical Constants Some Number-Theoretical Constants- Products of rational functions of p over primes, computed by Gerhard Niklasch and Pieter Moree. The On-Line Encyclopedia of Integer Sequences (OEIS) The On-Line Encyclopedia of Integer Sequences (OEIS)- Given an integer sequence, find its name, and formula. The Somos Sequence Site The Somos Sequence Site- Web resources for information on Somos sequences and related topics such as elliptic divisibility sequences. Active Elementary Number Theory Active Elementary Number Theory- Interactive (Javascript) expression of a number as a sum of two squares. Square-free Gaps Square-free Gaps- Algorithm and source code for the calculation of square-free numbers and gaps. An Introduction to the Theory of Numbers by Leo Moser An Introduction to the Theory of Numbers by Leo Moser- Textbook covering following topics: compositions and partitions; arithmetic functions; distribution of primes; irrational nu… A Mechanical Proof of Quadratic Reciprocity 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 Qu… Klein Polyhedra Klein Polyhedra- Examples and algorithms for computing Klein polyhedra, also known as Arnold sails or veils (voiles), by Keith Briggs. Covers, Sumsets and Zero-sums Covers, Sumsets and Zero-sums- A unified approach to covering systems, restricted sumsets and zero-sum problems by Zhi-Wei Sun. Lehmer's Conjecture Lehmer's Conjecture- That the Mahler measure of an algebraic number is bounded away from 1. Pages by Michael Mossinghoff, UCLA. Frequently Asked Questions Frequently Asked Questions- Number Theory section of the sci.math FAQ list. Fermat's Little Theorem Fermat's Little Theorem- With notes on Carmichael numbers and the life of R.D. Carmichael. Some Highlights of Arithmetic Combinatorics Some Highlights of Arithmetic Combinatorics- Lecture notes and resources on combinatorial number theory by Terence Tao. Introduction to Bernoulli Numbers 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). Number Theory Number Theory- Proofs along with equation solvers and graphical views written in Java. Hakmem Continued Fractions Hakmem Continued Fractions- Some notes from the MIT collection. Includes Gosper's algorithms for CF arithmetic. Number Theory Web Number Theory Web- Things of interest to number theorists collected by Keith Matthews. World Records for Numerical Palindromes World Records for Numerical Palindromes- The 196 Palindrome Quest and The Most Delayed Palindromic Number, by Jason Doucette. MathWorld Number Theory MathWorld Number Theory- Index to articles in Eric Weisstein's MathWorld in the area of number theory. MathPages: Number Theory MathPages: Number Theory- Articles by Kevin Brown on various topics in number theory. Somos Polynomials Somos Polynomials- Related to Somos sequences and elliptic theta functions. Vignettes on Automorphic and Modular forms, Representations, L-functions, and Number Theory Vignettes on Automorphic and Modular forms, Representations, L-functions, and Number Theory- By Paul Garrett. The Work of Robert Langlands The Work of Robert Langlands- Thesis, papers, manuscripts, letters and bibliography. The Arithmetic Properties of Binomial Coefficients The Arithmetic Properties of Binomial Coefficients- Activated text by Andrew Granville. The Valuation Theory Home Page 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.