Number Theory Web

Things of interest to number theorists collected by Keith Matthews.

http://www.numbertheory.org/ntw/

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.

http://www.russinoff.com/papers/gauss.html

Active Elementary Number Theory

Interactive (Javascript) expression of a number as a sum of two squares.

http://www.hbmeyer.de/taupaeng.htm

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.

http://www.trillia.com/moser-number.html

Covers, Sumsets and Zero-sums

A unified approach to covering systems, restricted sumsets and zero-sum problems by Zhi-Wei Sun.

http://math.nju.edu.cn/~zwsun/csz.htm

Fermat's Little Theorem

With notes on Carmichael numbers and the life of R.D. Carmichael.

http://www.pballew.net/FermLit.html

Frequently Asked Questions

Number Theory section of the sci.math FAQ list.

http://db.uwaterloo.ca/~alopez-o/math-faq/node21.html

Hakmem Continued Fractions

Some notes from the MIT collection. Includes Gosper's algorithms for CF arithmetic.

http://www.inwap.com/pdp10/hbaker/hakmem/cf.html

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).

http://numbers.computation.free.fr/Constants/Miscellaneous/bernoulli.html

Klein Polyhedra

Examples and algorithms for computing Klein polyhedra, also known as Arnold sails or veils (voiles), by Keith Briggs.

http://keithbriggs.info/klein-polyhedra.html

LMFDB

A handbook including tables, formulas, links, and references for L-functions and the underlying objects.

http://www.lmfdb.org/

Lehmer's Conjecture

That the Mahler measure of an algebraic number is bounded away from 1. Pages by Michael Mossinghoff, UCLA.

http://www.cecm.sfu.ca/~mjm/Lehmer/lc.html

MathPages: Number Theory

Articles by Kevin Brown on various topics in number theory.

http://www.mathpages.com/home/inumber.htm

MathWorld Number Theory

Index to articles in Eric Weisstein's MathWorld in the area of number theory.

http://mathworld.wolfram.com/topics/NumberTheory.html

Noncommutative Geometry, Trace Formulae and the Zeroes of the Riemann Zeta Function

Lecture notes by Alain Connes.

https://people.math.osu.edu/events/connes/Connes_course.html

Number Theory

Proofs along with equation solvers and graphical views written in Java.

http://www.alpertron.com.ar/NUMBERT.HTM

Some Highlights of Arithmetic Combinatorics

Lecture notes and resources on combinatorial number theory by Terence Tao.

http://www.math.ucla.edu/~tao/254a.1.03w/

Some Number-Theoretical Constants

Products of rational functions of p over primes, computed by Gerhard Niklasch and Pieter Moree.

http://www.gn-50uma.de/alula/essays/Moree/Moree.en.shtml

Somos Polynomials

Related to Somos sequences and elliptic theta functions.

http://grail.cba.csuohio.edu/~somos/somospol.html

Square-free Gaps

Algorithm and source code for the calculation of square-free numbers and gaps.

http://www.marmet.org/louis/sqfgap/index.html

The Arithmetic Properties of Binomial Coefficients

Activated text by Andrew Granville.

http://www.cecm.sfu.ca/organics/papers/granville/index.html

The On-Line Encyclopedia of Integer Sequences (OEIS)

Given an integer sequence, find its name, and formula.

http://oeis.org/

The Somos Sequence Site

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

http://faculty.uml.edu/jpropp/somos.html

The Work of Robert Langlands

Thesis, papers, manuscripts, letters and bibliography.

http://www.sunsite.ubc.ca/DigitalMathArchive/Langlands/intro.html

Transcendental Numbers

Maple worksheets, lecture notes and links to other resources by John Cosgrove.

http://staff.spd.dcu.ie/johnbcos/transcendental_numbers.htm

Vignettes on Automorphic and Modular forms, Representations, L-functions, and Number Theory

By Paul Garrett.

http://www.math.umn.edu/~garrett/m/v/

Visible Structures in Number Theory

By Peter Borwein and Loki Jrgenson. Recognising number patterns visually.

http://www.cecm.sfu.ca/~loki/Papers/Numbers/