Number theory

Build a solid foundation in the area of arithmetic groups and explore its inherent geometric and number-theoretical components.

This introductory textbook for graduate students presents modern developments in probabilistic number theory, many for the first time.

A friendly and concise introduction to the Mahler measure – a fascinating subject in contemporary mathematics.

This introductory textbook for graduate students presents modern developments in probabilistic number theory, many for the first time.

A mathematical record of bounded prime gaps breakthroughs, from Erdős to Polymath8, with linked computer programs and complete appendices.

A mathematical record of bounded prime gaps breakthroughs, from Erdős to Polymath8, with linked computer programs and complete appendices.

A guide to cryptanalysis and the implementation of cryptosystems, written for students and security engineers by leading experts.

Learn how to automatically prove mathematical statements in combinatorics, sequences, and number theory.

The continuation of an outstanding scholarly attempt to bring together all significant mathematical constants in one place.

This volume contains research papers in mathematical logic, particularly in model theory and its applications to algebra and formal theories of arithmetic.

Volume 2 of a two-volume introduction to the analytical aspects of automorphic forms, featuring proofs of critical results with examples.

Introduction to Diophantine approximation and equations focusing on Schmidt''s subspace theorem, with applications to transcendence.

A comprehensive treatment of block theory, emphasising cornerstones of the area which have not appeared in any book before.

A concise and comprehensive introduction to trace formula methods in the study of Shimura varieties and associated Galois representations.

This volume presents the proceedings of two major international meetings on mathematical logic held in Münster, Germany, in August 2002.

A concise and comprehensive introduction to trace formula methods in the study of Shimura varieties and associated Galois representations.

A step-by-step guide to Langlands'' early work leading up the Langlands Program for mathematicians and advanced students.

Volume 2 of a two-volume introduction to the analytical aspects of automorphic forms, featuring proofs of critical results with examples.

Comprehensive coverage of recent, exciting developments in Fourier restriction theory, including applications to number theory and PDEs.

The continuation of an outstanding scholarly attempt to bring together all significant mathematical constants in one place.

Comprehensive coverage of recent, exciting developments in Fourier restriction theory, including applications to number theory and PDEs.

A comprehensive treatment of block theory, emphasising cornerstones of the area which have not appeared in any book before.

Many of the best researchers and writers in discrete mathematics come together in a volume inspired by Ron Graham.

Discover how zeta and L-functions have shaped the development of major parts of mathematics over the past two centuries.

A comprehensive treatment of block theory, emphasising cornerstones of the area which have not appeared in any book before.

Discover how zeta and L-functions have shaped the development of major parts of mathematics over the past two centuries.

Many of the best researchers and writers in discrete mathematics come together in a volume inspired by Ron Graham.

A comprehensive treatment of block theory, emphasising cornerstones of the area which have not appeared in any book before.

This book highlights the many ideas and algorithms that Peter L.

This book highlights the many ideas and algorithms that Peter L.

This book investigates the influence of the graph of a symmetric matrix on the multiplicities of its eigenvalues.

A sweeping classification theory for computational counting problems using new techniques and theories.

A sweeping classification theory for computational counting problems using new techniques and theories.

A self-contained exposition of local class field theory for students in advanced algebra.

A self-contained exposition of local class field theory for students in advanced algebra.

A snapshot of the major renaissance happening today in the study of locally compact groups and their many applications.

Provides a comprehensive introduction to the theory of random orthogonal, unitary, and symplectic matrices.

Volume 1 of a two-volume introduction to the analytical aspects of automorphic forms, featuring proofs of critical results with examples.

Volume 1 of a two-volume introduction to the analytical aspects of automorphic forms, featuring proofs of critical results with examples.

This second volume of two presents analytic equivalents to the Riemann hypothesis.

This first volume of two presents classical and modern arithmetic equivalents to the Riemann hypothesis.

A thorough guide to elliptic functions and modular forms that demonstrates the relevance and usefulness of historical sources.

A thorough guide to elliptic functions and modular forms that demonstrates the relevance and usefulness of historical sources.

Detailed exposition of automorphic representations and their relation to string theory, for mathematicians and theoretical physicists.

Provides a novel interdisciplinary perspective on the state of the art of ultrametric pseudodifferential equations and their applications.

A graduate-level introduction to some of the important contemporary ideas and problems in the theory of moduli spaces.

A graduate-level introduction to some of the important contemporary ideas and problems in the theory of moduli spaces.

An exposition of the theory of curves over a finite field, and connections to the Riemann Hypothesis for function fields.

An exposition of the theory of curves over a finite field, and connections to the Riemann Hypothesis for function fields.

Now available in paperback for the first time; essential reading for all students of probability theory.