Directory of Number Theory Resources

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Number theory addresses problems about integer and rational numbers. It includes congruences, divisibility, primes, and Fermat's Last Theorem.

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• Algebraic
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• Diophantine Equations
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Resources in This Category

• A Mechanical Proof of Quadratic Reciprocity

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

• Active Elementary Number Theory

  http://www.hbmeyer.de/taupaeng.htm
  Interactive (Javascript) expression of a number as a sum of two squares.

• An Introduction to the Theory of Numbers by Leo Moser

  http://www.trillia.com/moser-number.html
  Textbook covering following topics: compositions and partitions; arithmetic functions; distribution of primes; irrational numbers; congruences; diophantine equations; combinatorial number theory; and geometry of numbers.

• Covers, Sumsets and Zero-sums

  http://math.nju.edu.cn/~zwsun/csz.htm
  A unified approach to covering systems, restricted sumsets and zero-sum problems by Zhi-Wei Sun.

• Fermat's Little Theorem

  http://www.pballew.net/FermLit.html
  With notes on Carmichael numbers and the life of R.D. Carmichael.

• Frequently Asked Questions

  http://db.uwaterloo.ca/~alopez-o/math-faq/node21.html
  Number Theory section of the sci.math FAQ list.

• Hakmem Continued Fractions

  http://www.inwap.com/pdp10/hbaker/hakmem/cf.html
  Some notes from the MIT collection. Includes Gosper's algorithms for CF arithmetic.

• Introduction to Bernoulli Numbers

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

  http://keithbriggs.info/klein-polyhedra.html
  Examples and algorithms for computing Klein polyhedra, also known as Arnold sails or veils (voiles), by Keith Briggs.

• Lehmer's Conjecture

  http://www.cecm.sfu.ca/~mjm/Lehmer/lc.html
  That the Mahler measure of an algebraic number is bounded away from 1. Pages by Michael Mossinghoff, UCLA.

• LMFDB

  http://www.lmfdb.org/
  A handbook including tables, formulas, links, and references for L-functions and the underlying objects.

• MathPages: Number Theory

  http://www.mathpages.com/home/inumber.htm
  Articles by Kevin Brown on various topics in number theory.

• MathWorld Number Theory

  http://mathworld.wolfram.com/topics/NumberTheory.html
  Index to articles in Eric Weisstein's MathWorld in the area of number theory.

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

  https://people.math.osu.edu/events/connes/Connes_course.html
  Lecture notes by Alain Connes.

• Number Theory

  http://www.alpertron.com.ar/NUMBERT.HTM
  Proofs along with equation solvers and graphical views written in Java.

• Number Theory Web

  http://www.numbertheory.org/ntw/
  Things of interest to number theorists collected by Keith Matthews.

• Some Highlights of Arithmetic Combinatorics

  http://www.math.ucla.edu/~tao/254a.1.03w/
  Lecture notes and resources on combinatorial number theory by Terence Tao.

• Some Number-Theoretical Constants

  http://www.gn-50uma.de/alula/essays/Moree/Moree.en.shtml
  Products of rational functions of p over primes, computed by Gerhard Niklasch and Pieter Moree.

• Somos Polynomials

  http://grail.cba.csuohio.edu/~somos/somospol.html
  Related to Somos sequences and elliptic theta functions.

• Square-free Gaps

  http://www.marmet.org/louis/sqfgap/index.html
  Algorithm and source code for the calculation of square-free numbers and gaps.

• The Arithmetic Properties of Binomial Coefficients

  http://www.cecm.sfu.ca/organics/papers/granville/index.html
  Activated text by Andrew Granville.

• The On-Line Encyclopedia of Integer Sequences (OEIS)

  http://oeis.org/
  Given an integer sequence, find its name, and formula.

• The Somos Sequence Site

  http://faculty.uml.edu/jpropp/somos.html
  Web resources for information on Somos sequences and related topics such as elliptic divisibility sequences.

• The Valuation Theory Home Page

  http://math.usask.ca/fvk/Valth.html
  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

  http://www.sunsite.ubc.ca/DigitalMathArchive/Langlands/intro.html
  Thesis, papers, manuscripts, letters and bibliography.

• Transcendental Numbers

  http://staff.spd.dcu.ie/johnbcos/transcendental_numbers.htm
  Maple worksheets, lecture notes and links to other resources by John Cosgrove.

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

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

• Visible Structures in Number Theory

  http://www.cecm.sfu.ca/~loki/Papers/Numbers/
  By Peter Borwein and Loki Jörgenson. Recognising number patterns visually.

• World Records for Numerical Palindromes

  http://www.jasondoucette.com/worldrecords.html
  The 196 Palindrome Quest and The Most Delayed Palindromic Number, by Jason Doucette.

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