Number theory

Noncompact symmetric and locally symmetric spaces naturally appear in many mathematical theories, including analysis (representation theory, nonabelian harmonic analysis), number theory (automorphic forms), algebraic geometry (modulae) and algebraic topology (cohomology of discrete groups).

Ever since the analogy between number fields and function fields was discovered, it has been a source of inspiration for new ideas, and a long history has not in any way detracted from the appeal of the subject.

Model theory is the meta-mathematical study of the concept of mathematical truth.

Model theory is the meta-mathematical study of the concept of mathematical truth.

Combinatorial research has proceeded vigorously in Russia over the last few decades, based on both translated Western sources and original Russian material.

Introduction to Modern Cryptography, the most relied-upon textbook in the field, provides a mathematically rigorous yet accessible treatment of this fascinating subject.

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Combinatorics meets number theory in this stimulating stroll through the zetas.

A systematic exposition of the basics of period domains.

An introduction to the analytic theory of automorphic forms in the case of fuchsian groups.

Deals with analytic number theory; many new results.

Monograph on most important topic in number theory.

A gem of a book bringing together 30 years worth of results that are certain to interest anyone whose research touches on quadratic forms.

Many classical and modern results and quadratic forms are brought together in this book.

This volume will be of lasting value to students and researchers working in this area.

This volume contains selected contributions from a very successful meeting on Number Theory and Dynamical Systems held at the University of York in 1987.

This book is a self-contained account of the one- and two-dimensional van der Corput method and its use in estimating exponential sums.

This book takes advanced graduate students from the foundations to topics on the research frontier.

Contributions by leading experts in the field provide a snapshot of current progress in polynomials and number theory.

Describes the arithmetic of modular forms and elliptic curves; self-contained and ideal for both graduate students and professional number theorists.

Lecture notes for graduates or researchers wishing to enter this modern field of research.

Timely collection of articles bringing together topics at the forefront of the theory, including the local Langlands programme and automorphic forms.

A collection of survey articles by leading young researchers, showcasing the vitality of Russian mathematics.

Provides a grounding in random matrix techniques applied to analytic number theory.

Conference proceedings based on the 1996 LMS Durham Symposium ''Galois representations in arithmetic algebraic geometry''.

Authoritative, up-to-date review of analytic number theory containing outstanding contributions from leading international figures.

State-of-the-art analytic number theory proceedings.

This book covers the whole spectrum of number theory, and is composed of contributions from some of the best specialists worldwide.

This is the fourteenth annual volume arising from the Seminaire de Theorie de Nombres de Paris covering the whole spectrum of number theory.

This book is concerned with the arithmetic of diagonal hypersurfaces over finite fields.

An elementary but detailed insight into the theory of L-functions.

Classic book, addressed to all lovers of number theory.

Discusses mathematics related to partitions of numbers into sums of positive integers.

Full account of Euler''s work on continued fractions and orthogonal polynomials; illustrates the significance of his work on mathematics today.

The real, rational, complex and p-adic numbers are discussed in detail in this comprehensive work.

Spencer Bloch''s landmark lectures are finally back in print, with a new preface by the author reflecting on recent developments.

Build paper polygons and discover how systematic paper folding reveals exciting patterns and relationships between seemingly unconnected branches of mathematics.

A self-contained 2010 account of the state of the art in classical complex multiplication.

Assuming little technical background, the author presents the strong analogies between these two concepts starting at an elementary level.

A classic text in number theory; this eighth edition contains new material on primality testing written by J.

A collection of articles presenting the state of the art in the topic of modular forms.

Modern and practical guide to higher dimensional sieve theory, with an Appendix describing methods for computing sieve functions.

Explains new applications of the ''large sieve'', an important tool of analytic number theory, presenting potential uses beyond this area.

An account of effective methods in transcendental number theory and Diophantine geometry by eminent authors.

The first book to give a complete treatment of rigid cohomology, from the basics to the very latest developments.

Graduate text/reference in number theory.

A 2006 text based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State.

An account of results extending Hilbert''s Tenth Problem to integrally closed subrings of global fields.

A monograph on Moonshine, a mathematical physics topic, for graduate students and researchers.