Descriptions of areas/courses in number theory, lecture notes
- The ABC Conjecture
- Reken mee met ABC (Bart de Smit, Gillien Geuze), Nieuw Archief voor Wiskunde (5th series) 8 (2007), 26-30
- Reken Mee met ABC
- Historical comments by David Masser and Joseph Oesterlé on the origins of the ABC conjecture
- The ABC-conjecture, Frits Beukers, ABC-day, Leiden, September 9, 2005 (fritsABCpresentation.pdf)
- ABC@home (finding abc triples related to the ABC conjecture)
- Special day on the ABC-conjecture, Intercity Number Theory Seminar, September 9th 2005
- It's As Easy As abc, Andrew Granville and Thomas J. Tucker, AMS Notices, November 2002, 49
- The ABC Conjecture Home Page (Abderrahmane Nitaj)
- Arithmetical Geometry
- Videos of lectures, Clay Mathematics Institute 2006 Summer School on Arithmetic Geometry, July 17-August 11, 2006, Mathematisches Institut, Georg-August-Universität, Göttingen
- Topics in Arithmetical Geometry (Outline of a course by Shou-Wu Zhang - pdf)
- Grothendieck's SGA
- Differential algebraic geometry, a scheme theoretic approach (lecture notes by Henri Gillet, 1998)
- Lecture notes on the local Langlands correspondence (Michael Harris)
- Modular Mahler Measures, slides by Fernando Villegas
- Course notes on Heights, (Nils-Peter Skoruppa)
- Diophantine geometry in characteristic p: a survey, (Felipe Voloch)
- Draft of PCMI Lecture Notes on Open Questions in Arithmetic Algebraic Geometry (Alice Silverberg) (ps file 803K)
- Lecture Notes from H.L. Lenstra's Algebraic Curves Math 274, 1995
- Fermat's Last Theorem
- Links to articles on Fermat's Last Theorem, James Propp
- Irregular primes (Jared Weinstein)
- Computing irregular primes
- A proof of the full Shimura-Taniyama-Weil conjecture is announced, Henri Darmon, Notices of the AMS, December 1999
- William Hammond's Fermat Archive
- Charles Daney's pages on Fermat's last Theorem
- Notes on Fermat's Last Theorem, A.J. van der Poorten, Canadian Mathematical Society Series of Monographs and Advanced Texts, Wiley-Interscience, January, 1996, ISBN 0-471-06261-8
- On a Generalized Fermat-Wiles Equation, (Steve Finch)
- The Solving of Fermat's Last Theorem, Karl Rubin, Ohio State University Distinguished Lecture May 22, 1997
- Le Théorème de Fermat (Karim Belabas and Catherine Goldstein)
- Irregular primes
- Pell equations
- Primes and factoring
- Expository article on the recent theorem of Goldston, Pintz, and Yildirim on small gaps between prime numbers, K. Soundararajan; also see note on P.X. Gallagher's result on the singular series by Kevin Ford
- The Challenge of Large Numbers (Richard Crandall)
- The ECMNET Project
- Small gaps between prime numbers: The work of Goldston-Pintz-Yildirim, K. Soundararajan, Bulletin Amer. Math. Soc. 44 (2007), 1-18
- Small gaps between primes, transparencies of a talk by Jimena Sivak-Fischler
- The Green-Tao Theorem on k-term AP's among the primes (an introduction) (pdf)
- Prime constellation records (Jens Kruse Andersen)
- Primzahlbeweise
- primes of the form x2+ny2 (Marios Magioladitis)
- The Green-Tao Theorem on arithmetic progressions in the primes: an ergodic point of view, Bryna Kra, Bull. Amer. Math. Soc. 43 (2006), 3-23
- About the cover: On the distribution of primes-Gauss' tables, Yuri Tschinkel, Bull. Amer. Math. Soc. 43 (2006), 89-91
- The Niven Lectures, (Carl Pomerance) March 21-23, 2005, University of British Columbia
- It is easy to determine whether a given integer is prime, Andrew Granville, Bull. Amer. Math. Soc. 42 (2005), 3-38
- Generalized Fermat Primes Search
- PRIMES is in P- a non-specialist account by Folkmar Bornemann
- Exposition of the Primes is in P theorem (Kevin Ford)
- Review of Prime numbers: A computational perspective, Reviewer: Jeremy Teitelbaum
- The Prime Pages
- The Nth prime page
- Largest Known Primes
- Mersenne Primes: History, Theorems and Lists
- Generalised Mersenne primes (Wojciech Florek)
- MacTutor History of Mathematics: Prime Numbers
- Mersenne Prime Search;
Gordon Spence's Mersenne prime discovery
- Will Edgington's Mersenne Primes Page
- AMS Notices article on Primality Testing (Richard Pinch)
- Frobenius Pseudoprimes (Jon Grantham)
- Numbers of the form k·2n ± 1 (Joe McLean)
- Primes of the form k·2n+1 (Ray Ballinger and Wilfred Keller)
- Primes of the form k·2n-1 (Wilfred Keller)
- Hans Riesel's problem (Ray Ballinger and Wilfred Keller)
- Sierpinski's problem (Ray Ballinger and Wilfred Keller)
- Seventeen or Bust, a distributed attack on the Sierpinski problem, Seventeen Or Bust wiki
- Fermat number factoring status (Wilfred Keller)
- Appendix 1: Factorization results (Hisanori Mishima)
- Factorizations of Cyclotomic Numbers (Mitsuo Morimoto)
- Factorization of Generalized Repunits (Andy Steward)
- All known factors of 30+ digits found by Pollard's p-1 method (Andy Steward)
- Repunit primes and factors of 10n±1 (Torbjörn Granlund)
- Surprising connections between prime numbers and physics (Matthew Watkins)
- The largest known composite Fermat number (John Cosgrave)
- Lucas-Lehmer criterion (Paul Garrett)
- Cullen and Woodall numbers (Paul Leyland)
- Factorizations of xy + yx for 1 < y < x < 101 (Andrey Kulsha)
- Links to factoring programs (Andrey Kulsha)
- Prime number theorem
- Complex Variables, by Robert Ash and W.P. Novinger has a chapter on the prime number theorem
- Prime gaps
- Sums of integer cubes
- Table of non-negative integral solutions of n=x3+y3+z3 (Hisanori Mishima)
- Twin primes
- Elliptic Curves
- Finding meaning in error terms, Barry Mazur, Bulletin of the AMS, 45 (2008), 185-228
- The DLP on Elliptic Curves with the same order, Marios Magioladitis
- Ribet-Stein notes on Serre's conjecture (pdf)
- A normal form for elliptic curves, Harold Edwards, Bull. Amer. Math. Soc. 44 (2007), 393-422
- Math 583 at University of Washington: The Birch and Swinnerton-Dyer Conjecture, lecture course (William Stein)
- Average ranks of elliptic curves, Baur Bektemirov, Barry Mazur, William Stein and Mark Watkins
- Some interesting references on elliptic curves (Mark Joye)
- Student Projects (elliptic curves)
- Elliptic curves over Q (pdf) (Steve Finch)
- PlanetMath account of arithmetic of elliptic curves (Alvaro Lozano-Robledo)
- DEA 2003/04: Elliptic functions and elliptic curves, lecture notes by Jan Nekovář
- Elliptic curves in recreational number theory (Allan Macleod)
- E.R. Hedrick Lectures of the MAA, August 2003: Rational points on modular elliptic curves (Henri Darmon)
- X0(11) and X1(11), the Euler system of Heegner points (Tom Weston)
- An Elementary Introduction to Elliptic Curves (ps), Leonard S. Charlap, David P. Robbins, 1988, 1990
- Ranks of elliptic curves, K. Rubin, A. Silverberg, Bull. AMS. 39, 2002, 455-474
- Review of Euler Systems, Reviewer: Henri Darmon
- The arithmetic of elliptic curves and diophantine equations (Loic Merel)
- Computing the rank of an elliptic curve, Undergraduate thesis, Jeff Achter, Brown University 1992
- Hyperelliptic curves allowing fast arithmetic (Tanya Lange)
- Elliptische Kurven und komplexe Multiplikation, Annegret Weng (ps)
- Draft chapters of elliptic curve handbook ECH1
- History of elliptic curves rank records (Andrej Dujella)
- High rank elliptic curves with prescribed torsion (Andrej Dujella)
- Stéfane Fermigier's Page on Elliptic curves
- References to Elliptic Curves
- Course Notes by Jim Milne: Algebraic number theory, Class field theory, Algebraic Geometry, Elliptic Curves, Modular functions and forms, Abelian varieties, Etale Cohomology
- Seminar Notes on Elliptic Curves and Formal Groups: J. Lubin, J.-P. Serre and J. Tate, Summer Institute on Algebraic Geometry, Woods Hole, 1964
- Tables accompanying Rational eigenvectors in spaces of ternary forms, Larry Lehman, Math. Comp. 66 (1997) 833-839
- Seminar notes: Aspects of complex multiplication (Don Zagier), An introduction to group schemes (René Schoof), notes by John Voight
- Math 574, (An introduction to rational points on elliptic curves through examples of interesting elliptic curves), Jerrold Tunnell
- Elliptische Kurven, Lecture notes by Franz Lemmermeyer
- Elliptic curve source material (Franz Lemmermeyer)
- The Modular curves X0(N), Lecture notes by Bas Edixhoven
- Elliptic curves and right triangles (slides by Karl Rubin)
- Algebraic Number Theory
- Ideal class groups, class numbers and discriminants (Alvaro Lozano-Robledo)
- Dedekind zeta function, notes by Ben Brubaker
- PlanetMath account of algebraic number theory (Alvaro Lozano-Robledo)
- Expository notes on algebraic number theory, eg. Kummer's Lemma (Keith Conrad)
- On a theorem of Jordan, J.-P. Serre, Bull. Amer. Math. Soc. 40 (2003) 429-440
- The idelic approach to number theory, introduction to local fields, the modular curves X0(11) and X1(11) (Tom Weston)
- Oberwolfach: Explicit Algebraic Number Theory, Notes by John Voight
- How many fields share a common discriminant? (Daniel Mayer)
- Cubic number Fields (Daniel A. Mayer)
- Review of Cohomology of Number Fields, J. Neukirch, A. Schmidt, K. Wingberg (Reviewer: F.Q. Gouvêa) Bulletin AMS 39, 101-107, 2002
- Online Seminar: Galois theory of p-extensions (a study of the book Galoissche Theorie der p-Erweiterungen, Springer 1970, by Helmut Koch)
- Galois modules in arithmetic, by Boas Erez
- MAS4002: Algebraic Number Theory, Course notes by Robin Chapman, University of Exeter
- Survey of Euclidean Number Fields (ps file 371K) (Franz Lemmermeyer)
- Quadratische Zahlkörper, Lecture notes by Franz Lemmermeyer
- Richard Mollin's Quadratic Fields Research Area
- Dan Bernstein's Math 514
- Course Note: Algebraic number theory, Class field theory, Algebraic Geometry, Elliptic Curves, Modular functions and forms, Abelian varieties, Etale Cohomology
- Binary Cubic Forms and Cubic Number Fields
- The Cyclotomic Fields Virtual Study Group
- Course Notes for elementary and algebraic number theory, Ivan Fesenko
- The Nonabelian Reciprocity Law for Local Fields, Jonathan Rogawski, Notices AMS, Vol 47, 2000
- Algebraic Number Theory and commutative algebra, lecture notes by Robert Ash
- Math 254B (Number Theory), lecture notes on class field theory, abelian extensions of number fields etc (Kiran Kedlaya)
- Algebraic Number Theory and Automorphic L-functions, lecture notes by Ching-Li Chai
- L-functions, Modular Forms, Automorphic Forms
- Review by Stephen Gelbart of Advanced Analytic Number Theory: L-Functions, Carlos Moreno
- Artin L-Functions: A Historical Approach, (Noah Snyder)
- L-functions of abelian varieties (Jared Weinstein)
- Modular forms of weight 1 (Marios Magioladitis)
- Modular forms over SL2(Q) (pdf) (Steve Finch)
- The principle of functoriality, James Arthur, BAMS 40 39-53, 2003
- Modular Forms and Dirichlet Series, Andrew Ogg, W.A. Benjamin, NY. 1969
- Review of Arithmeticity in the theory of automorphic forms, Reviewer: Hiroyuki Yoshida
- Math 574 - A Graduate course in automorphic forms and representations (Stephen Miller)
- Database of Automorphic L-functions (Stephen Miller)
- The idelic approach to number theory, introduction to local fields, the modular curves X0(11) and X1(11), L-functions and cyclotomic units, the Euler system of Heegner points (expository papers by Tom Weston)
- Modular forms (Igor Dolgachev)
- Modular forms database, by William Stein
- L-functions and cyclotomic units (Tom Weston)
- Paul Garrett
- Ken Ribet's Modular Forms and Hecke Operators Course (Notes by William A. Stein)
- Some Old Problems and New Results about Quadratic Forms, W. Duke, Notices of the AMS, February 1997
- L-functions of the Selberg class S (Brian Conrey)
- Mahler measure
- Analytic Number Theory
- Computational Number Theory
- Congruent Numbers
- Well-known constants
- Diophantine Approximation, Diophantine equations, Geometry of Numbers, Irrationality
- Lectures from AWS 2008: Special Functions and Transcendence in pdf and video format
- Undecidability in Number Theory, Bjorn Poonen, Notices AMS 55, 2008
- An introduction to irrationality and transcendence methods, course and project outline, draft lecture notes for lectures 1, 2, 3, 5, Arizona Winter School 2008, Michel Waldschmidt
- Introduction to Diophantine methods: irrationality and transcendence, course notes by Michel Waldschmidt
- Algebraic and Transcendental Numbers (Stéphane Fischler)
- Questions d'irrationalité (et de transcendance): hier et aujourd'hui, (Michel Waldschmidt)
- Table of approximations to π = 3.14159··· of the form a/b2 (Ismael Jiménez Calvo)
- Second thoughts on some topics from Diophantine approximation and analytic number theory (Cameron Stewart) - item 12 of "Publications in refereed journals and books"
- zeta(3) (Jared Weinstein)
- papers on irrationality of certain constants (Stéphane Fischler
- Hilbert's tenth problem page
- Criteria for irrationality of Euler's constant (Jonathan Sondow)
- Multiple Zeta Values and Euler-Zagier Numbers, etc. (Michel Waldschmidt)
- Zeta values on the Web (Wadim Zudilin)
- Diophantine m-tuples (Andrej Dujella)
- Catalogue of Surfaces (Ronald van Luijk)
- A bibliography of papers related to simultaneous diophantine approximation (Keith Briggs)
- Linear Independence Measures for Logarithms of Algebraic Numbers, (Cetraro lectures of Michel Waldschmidt, July 2000)
- Online integer relations interface (CECM, Simon Fraser University)
- Perfect Lattices (Jacques Martinet and Christian Batut)
- Review of J. Martinet's Perfect lattices in Euclidean spaces, by Gabriele Nebe
- Nombres irrationels, nombres transcendants, Édouard Lebeau, Journal de Maths des Élèves 3, 1995
- Gisbert Wüstholz: Ausgewählte Kapitel der Zahlentheorie und der Geometrie, Vorläufige unvollständige Version, WS 1995/96
- Thue equations (Clemens Heuberger)
- Publications of Benne de Weger
- A new extreme abc-example (Benne de Weger)
- Diophantine Approximations, Mathematical Transactions 2 (1996) A Collection of papers dedicated to the memory of Prof. N.I. Feldman
- Lattices in Cryptography and Cryptanalysis (Daniele Micciancio)
- Quadratic reciprocity
- Squarefree numbers
- Abundant numbers
- Aliquot sequences, Perfect, Amicable numbers
- Bell Numbers
- Bernoulli Numbers
- Congruences
- Continued Fractions
- 3x+1
- Valuations
- Primitive roots and Artin's conjecture
- Fibonacci numbers
- Function fields
- Goldbach's Conjecture
- Hall's Conjecture
- Kurepa's Conjecture
- The Riemann Hypothesis
- Voronin Universality Theorem (Jörn Steuding-MathWorld)
- Guy Robin's theorem on the Riemann hypothesis
- On Robin's criterion for the Riemann Hypothesis (YoungJu Choie, Nicholas Lichiardopol, Pieter Moree, Patrick Solé); also see 70 % de RH
- Abundant Numbers and the Riemann Hypothesis (Keith Briggs, Experimental Math. 15, Issue 2 (2006), 251-256)
- SIMUW 2007: What is Riemann's Hypothesis? (A course for high school students)
- Problems of the Millennium: The Riemann Hypothesis Peter Sarnak, 2004
- Turing and the Riemann Hypothesis, Andrew Booker, Notices of the AMS., 53 (2006) 1208-1211
- Zeroes of the Riemann zeta function and Dirichlet L-functions
- Further systematic computations on the summatory function of the Möbius function, Tadej Kotnik, Jan van de Lune
- Riemann's zeta function and beyond, Stephen Gelbart, Stephen Miller, Bull. AMS 41 (2004), 59-112
- The Riemann Hypothesis, B. Conrey, Notices of the AMS, 341-353, March 2003
- Directory of zetafunctions (Matthew Watkins)
- Noncommutative Geometry, Trace Formulas and the Zeros of the Riemann Zeta Function, a course by Alain Connes
- Links to Riemann's original paper
- Introduction to the Riemann Zeta function (Xavier Gourdon and Pascal Sebah)
- Tables of zeros of the zeta function (Andrew Odlyzko)
- The Riemann zetafunction and its relatives (Frits Beukers) (ps file)
- The Riemann Hypothesis in a Nutshell (Glen Pugh)
- Distribution Modulo 1
- Number Theory and Cryptography
- Introductory Number Theory
- Extremal Functions in Fourier Analysis
- Descriptions of Interesting Courses
- Lehmer's Problem:
- Markov numbers:
- Practical numbers:
- PV numbers (Pisot-Vijayaraghavan and Salem numbers):
- Review by M. Mendes France: Pisot and Salem numbers, M.J. Bertin, A. Decomps-Guilloux, M. Grandet-Hugot, M. Pathiaux-Delefosse, J. P. Schreiber, Birkhäuser 1992, ISBN 0-8176-2648-4, Bull. Amer. Math. Soc. 29 (1993) 274-278
- The arithmetic and geometry of Salem numbers, E. Ghate and E. Hironaka, Bulletin AMS 38 (2001), 293-314
- Binomial Coefficients: Andrew Granville's Page
- Equal Sums of Like Powers/Tarry Escott Problem: Chen Shuwen's Page
- Integer Sequences, Well-known Functions
- Selberg's Eigenvalue Conjecture:, Peter Sarnak, Notices of the AMS, November 1995
- Fermat Quotient
- Erdös-Strauss conjecture
- Exponential sums
- p-adic numbers
- Partitions
- Problems
- Combinatorial number theory
- Sieve theory
- Visualizing the Sieve of Eratosthenes, David N. Cox, AMS Notices, May 2008, 55
- A Tale of Two Sieves, C. Pomerance, AMS Notices, December 1996
- Notes on sieve methods, notes by Robert Juricevic based on 6 lectures by Ram Murty (ps file 517K)
- Sieves in number theory, by George Greaves, Reviewer H. Halberstam, Bull. AMS. 40, 2003, 109-119
- Sieve Methods, Masters Thesis, Denis Xavier Charles, SUNY Buffalo 2000 (pdf 501K)
- Ben Green's notes
- Carmichael numbers
- Catalan's conjecture
- Class number
Various other numbers
- Recreations in Number Theory
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Last modified 29th April 2008