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Reciprocity laws of various kinds play a central role in number theory. In the easiest case, one obtains a transparent formulation by means of roots of unity, which are special …
Written for advanced undergraduate and first-year graduate students, this book aims to introduce students to a serious level of p-adic analysis with important implications for …
This book seeks to describe the rapid development in recent decades of sieve methods able to detect prime numbers. The subject began with Eratosthenes in antiquity, took on new …
A look at one of the most exciting unsolved problems in mathematics todayElliptic Tales describes the latest developments in number theory by looking at one of the most exciting …
The remarkable properties of the numbers one through nineIn Single Digits, Marc Chamberland takes readers on a fascinating exploration of small numbers, from one to nine, looking …
This book introduces a new class of non-associative algebras related to certain exceptional algebraic groups and their associated buildings. Richard Weiss develops a theory of …
An outrageous graphic novel that investigates key concepts in mathematicsIntegers and permutations-two of the most basic mathematical objects-are born of different fields and …
An especially timely work, the book is an introduction to the theory of p-adic L-functions originated by Kubota and Leopoldt in 1964 as p-adic analogues of the classical …
The results established in this book constitute a new departure in ergodic theory and a significant expansion of its scope. Traditional ergodic theorems focused on amenable groups, …
An entertaining and enlightening history of irrational numbers, from ancient Greece to the twenty-first centuryThe ancient Greeks discovered them, but it wasn't until the …