Number Theory

This monograph elucidates and extends many theorems and conjectures in analytic number theory and algebraic asymptotic analysis via the natural not...

This is an invaluable book that presents the original work published in French, in 1904, by Henry Leon Lebesgue, the creator of the theory of integ...

This book continues the applications of mathematics, more specifically of theta, eta, and zeta functions, and modular forms, to various areas of th...

The two works titled What Are and What Should the Numbers Be? (1888) and Continuity and Irrational Numbers (1872) are Dedekind's contributions to t...

The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutat...

Although the Lucas sequences were known to earlier investigators such as Lagrange, Legendre and Genocchi, it is because of the enormous number and ...

This monograph explores the finiteness and structure of Shafarevich-Tate groups of abelian varieties over global fields of any characteristic. Read...

Understanding the natural numbers, which we use to count things, comes naturally. Meanwhile, the real numbers, which include a wide range of number...

Understanding the natural numbers, which we use to count things, comes naturally. Meanwhile, the real numbers, which include a wide range of number...

This volume contains the proceedings of the 2019 Lluis A. Santalo Summer School on $p$-Adic Analysis, Arithmetic and Singularities, which was held ...

Mathematical Theory of Fuzzy Sets presents the mathematical theory of non-normal fuzzy sets such that it can be rigorously used as a basic tool to ...

Our grasp of numbers and uncertainty is one of humankind's most distinctive and important traits. It is pivotal to our exceptional ability to contr...

Elementary Number Theory takes an accessible approach to teaching students about the role of number theory in pure mathematics and its important ap...

Originally published in 1994, The Incommensurability Thesis is a critical study of the Incommensurability Thesis of Thomas Kuhn and Paul Feyerabend...

A selection of the most accessible survey papers from the Millennial Conference on Number Theory. Presented and compiled by a group of internationa...

This book is an introduction to the theory of algebraic numbers and algebraic functions of one variable. The basic development is the same for bot...

Catalan numbers, named after the French-Belgian mathematician Eugène Charles Catalan (1814-1894), arise in a variety of combinatorial problems. The...

This carefully prepared manuscript presents elimination theory in weighted projective spaces over arbitrary noetherian commutative base rings. Elim...

From Polynomials to Sums of Squares describes a journey through the foothills of algebra and number theory based around the central theme of factor...

This is the proceedings of the conference 'Primitive Forms and Related Subjects' held at Kavli IPMU, the University of Tokyo in February 10-14, 201...

An indispensable resource for readers in physics and mathematics seeking a solid grasp of the mathematical tools shaping modern theoretical physics...

This proceedings volume, the sixth in a series from the Combinatorial and Additive Number Theory (CANT) conferences, is based on talks from the 20t...

The aim of this book is to give an introduction to what has come to be known as Standard Monomial Theory (SMT). SMT deals with the construction of ...

This volume collects the texts of five courses given in the Arithmetic Geometry Research Programme 2009-2010 at the CRM Barcelona. All of them deal...

This book seeks to describe the rapid development in recent decades of sieve methods able to detect prime numbers. The subject began with Eratosthe...

Alexander Grothendieck is often considered one of the greatest mathematicians of the twentieth century (if not all time), and his unique vision con...

Updated to reflect current research and extended to cover more advanced topics as well as the basics, Algebraic Number Theory and Fermats Last Theo...

Updated to reflect current research and extended to cover more advanced topics as well as the basics, Algebraic Number Theory and Fermats Last Theo...

Eduard Wirsing was an outstanding number theorist. In his research he made significant contributions to various subfields of number theory and also...

This book is a concise, self-contained treatise on abstract algebra with an introduction to number theory, where students normally encounter rigoro...

This book presents cutting-edge research, advanced techniques, and practical applications of Algebra Analysis and Topology. It offers in-depth insi...

This introductory text is designed for undergraduate courses in number theory, covering both elementary number theory and analytic number theory. T...