Mathematics/Number theory

Subject Classification

AMS: Number theory

2025

Universal Pairs for Diophantine Equations

by Marco David, Théo André, Mathis Bouverot-Dupuis, Eva Brenner, Loïc Chevalier, Anna Danilkin, Charlotte Dorneich, Kevin Lee, Xavier Pigé, Timothé Ringeard, Quentin Vermande, Paul Wang, Annie Yao, Zhengkun Ye and Jonas Bayer

Jul 29

Farey Sequences and Ford Circles

by Lawrence C. Paulson

May 15

Sophie Germain’s Theorem

by Benoît Ballenghien

Apr 09

2024

Theta Functions

by Manuel Eberl

Dec 02

The Rogers–Ramanujan Identities

by Manuel Eberl

Dec 02

Combinatorial q-Analogues

by Manuel Eberl

Dec 02

The Sum-of-Squares Function and Jacobi's Two-Square Theorem

by Manuel Eberl

Nov 26

Wooley's Discrete Inequality

by Angeliki Koutsoukou-Argyraki

Oct 02

Concrete bounds for Chebyshev’s prime counting functions

by Manuel Eberl

Sep 13

Prime Number Theorem with Remainder Term

by Shuhao Song and Bowen Yao

May 05

Kummer's congruence

by Manuel Eberl

Mar 20

Wieferich–Kempner Theorem

by Jamie Chen

Mar 06

2023

Polygonal Number Theorem

by Kevin Lee, Zhengkun Ye and Angeliki Koutsoukou-Argyraki

Aug 10

Zeckendorf’s Theorem

by Christian Dalvit

Jun 12

Three Squares Theorem

by Anna Danilkin and Loïc Chevalier

May 03

Positional Notation for Natural Numbers in an Arbitrary Base

by Charles Staats

Apr 03

2022

p-adic Fields and p-adic Semialgebraic Sets

by Aaron Crighton

Sep 22

From THE BOOK: Two Squares via Involutions

by Maksym Bortin

Aug 15

Diophantine Equations and the DPRM Theorem

by Jonas Bayer, Marco David, Benedikt Stock, Abhik Pal, Yuri Matiyasevich and Dierk Schleicher

Jun 06

Digit Expansions

by Jonas Bayer, Marco David, Abhik Pal and Benedikt Stock

Apr 20

Irrational numbers from THE BOOK

by Lawrence C. Paulson

Jan 08

2021

Lifting the Exponent

by Maya Kądziołka

Apr 27

Hensel's Lemma for the p-adic Integers

by Aaron Crighton

Mar 23

The Hermite–Lindemann–Weierstraß Transcendence Theorem

by Manuel Eberl

Mar 03

2020

Amicable Numbers

by Angeliki Koutsoukou-Argyraki

Aug 04

Irrationality Criteria for Series by Erdős and Straus

by Angeliki Koutsoukou-Argyraki and Wenda Li

May 12

Gaussian Integers

by Manuel Eberl

Apr 24

Lucas's Theorem

by Chelsea Edmonds

Apr 07

Furstenberg's topology and his proof of the infinitude of primes

by Manuel Eberl

Mar 22

Arithmetic progressions and relative primes

by José Manuel Rodríguez Caballero

Feb 01

Mersenne primes and the Lucas–Lehmer test

by Manuel Eberl

Jan 17

2019

The Irrationality of ζ(3)

by Manuel Eberl

Dec 27

Gauss Sums and the Pólya–Vinogradov Inequality

by Rodrigo Raya and Manuel Eberl

Dec 10

The Transcendence of Certain Infinite Series

by Angeliki Koutsoukou-Argyraki and Wenda Li

Mar 27

Elementary Facts About the Distribution of Primes

by Manuel Eberl

Feb 21

Probabilistic Primality Testing

by Daniel Stüwe and Manuel Eberl

Feb 11

2018

The Transcendence of π

by Manuel Eberl

Sep 28

The Prime Number Theorem

by Manuel Eberl and Lawrence C. Paulson

Sep 19

Pell's Equation

by Manuel Eberl

Jun 23

Irrational Rapidly Convergent Series

by Angeliki Koutsoukou-Argyraki and Wenda Li

May 23

2017

Dirichlet L-Functions and Dirichlet's Theorem

by Manuel Eberl

Dec 21

Homogeneous Linear Diophantine Equations

by Florian Messner, Julian Parsert, Jonas Schöpf and Christian Sternagel

Oct 14

The Hurwitz and Riemann ζ Functions

by Manuel Eberl

Oct 12

Dirichlet Series

by Manuel Eberl

Oct 12

Minkowski's Theorem

by Manuel Eberl

Jul 13

Bernoulli Numbers

by Lukas Bulwahn and Manuel Eberl

Jan 24

Bertrand's postulate

by Julian Biendarra and Manuel Eberl

Jan 17

The Transcendence of e

by Manuel Eberl

Jan 12

2015

The Divergence of the Prime Harmonic Series

by Manuel Eberl

Dec 28

Liouville numbers

by Manuel Eberl

Dec 28

The Stern-Brocot Tree

by Peter Gammie and Andreas Lochbihler

Dec 22

2013

Pratt's Primality Certificates

by Simon Wimmer and Lars Noschinski

Jul 22

Lehmer's Theorem

by Simon Wimmer and Lars Noschinski

Jul 22

2009

Perfect Number Theorem

by Mark Ijbema

Nov 22

2007

Sums of Two and Four Squares

by Roelof Oosterhuis

Aug 12

Fermat's Last Theorem for Exponents 3 and 4 and the Parametrisation of Pythagorean Triples

by Roelof Oosterhuis

Aug 12