Number Theory

Hilbert's tenth problem is one of 23 problems proposed by David Hilbert in 1900 at the International Congress of Mathematicians in Paris. These pro...

Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Probability through Algebra is based on a course of...

Introduced by Peter Scholze in 2011, perfectoid spaces are a bridge between geometry in characteristic 0 and characteristic $p$, and have been used...

When Leonhard Euler first arrived at the Russian Academy of Sciences, at the age of 20, his career was supported and promoted by the Academys secre...

Joseph Liouville is recognised as one of the great mathematicians of the nineteenth century, and one of his greatest achievements was the introduct...

Famous mathematical constants include the ratio of circular circumference to diameter, = 3.14 , and the natural logarithm base, e = 2.718 . Studen...

The Woods Hole trace formula is a Lefschetz fixed-point theorem for coherent cohomology on algebraic varieties. It leads to a version of the sheave...

The Mahler measure is a fascinating notion and an exciting topic in contemporary mathematics, interconnecting with subjects as diverse as number th...

Searching for small gaps between consecutive primes is one way to approach the twin primes conjecture, one of the most celebrated unsolved problems...

This is a collection of lecture notes from the minicourses in the December 2018 Langlands Workshop: Endoscopy and Beyond. The volume combines seven...

The striking theorems showcased in this book are among the most profound results of twentieth-century analysis. The authors' original approach comb...

ANTS-IX was the ninth edition of the biennial International Symposium on Algorithmic Number Theory. The ?rst edition of this symposium was held at ...

This revised and enlarged sixth edition of Proofs from THE BOOK features an entirely new chapter on Van der Waerdens permanent conjecture, as well ...

This volume contains research and expository content based on a wide variety of topics within modern number theory and arithmetic geometry. Researc...