Number theory

This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional theory of complex dimensions, valid for arbitrary bounded subsets of Euclidean spaces, as well as for their natural generalization, relative fractal drums.

Now in its second edition, this textbook provides an introduction and overview of number theory based on the density and properties of the prime numbers.

Featuring the work of twenty-three internationally-recognized experts, this volume explores the trace formula, spectra of locally symmetric spaces, p-adic families, and other recent techniques from harmonic analysis and representation theory.

This book consists of both expository and research articles solicited from speakers at the conference entitled "e;Arithmetic and Ideal Theory of Rings and Semigroups,"e; held September 22-26, 2014 at the University of Graz, Graz, Austria.

This is a self-contained exposition by one of the leading experts in lattice theory, George Gratzer, presenting the major results of the last 70 years on congruence lattices of finite lattices, featuring the author's signature Proof-by-Picture method.

This book contains a compendium of 25 papers published since the 1970s dealing with pi and associated topics of mathematics and computer science.

The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics.

This monograph provides an accessible and comprehensive introduction to James Arthur's invariant trace formula, a crucial tool in the theory of automorphic representations.

In this monograph, the authors develop a new theory of p-adic cohomology for varieties over Laurent series fields in positive characteristic, based on Berthelot's theory of rigid cohomology.

Exploring the interplay between deep theory and intricate computation, this volume is a compilation of research and survey papers in number theory, written by members of the Women In Numbers (WIN) network, principally by the collaborative research groups formed at Women In Numbers 3, a conference at the Banff International Research Station in Banff, Alberta, on April 21-25, 2014.

This expanded textbook, now in its second edition, is a practical yet in depth guide to cryptography and its principles and practices.

Featuring the clearly presented and expertly-refereed contributions of leading researchers in the field of approximation theory, this volume is a collection of the best contributions at the Third International Conference on Applied Mathematics and Approximation Theory, an international conference held at TOBB University of Economics and Technology in Ankara, Turkey, on May 28-31, 2015.

This book collects more than thirty contributions in memory of Wolfgang Schwarz, most of which were presented at the seventh International Conference on Elementary and Analytic Number Theory (ELAZ), held July 2014 in Hildesheim, Germany.

Presentingthe first systematic treatment of the behavior of Neron models under ramifiedbase change, this book can be read as an introduction to various subtleinvariants and constructions related to Neron models of semi-abelian varieties,motivated by concrete research problems and complemented with explicitexamples.

"e;The son of a prominent Japanese mathematician who came to the United States after World War II, Ken Ono was raised on a diet of high expectations and little praise.

Over the last forty years, David Vogan has left an indelible imprint on the representation theory of reductive groups.

This textbook effectively builds a bridge from basic number theory to recent advances in applied number theory.

This volume contains a collection of research and survey papers written by some of the most eminent mathematicians in the international community and is dedicated to Helmut Maier, whose own research has been groundbreaking and deeply influential to the field.

This book focuses on complex geometry and covers highly active topics centered around geometric problems in several complex variables and complex dynamics, written by some of the world's leading experts in their respective fields.

This book, written by an accomplished female mathematician, is the second to explore nonstandard mathematical problems - those that are not directly solved by standard mathematical methods but instead rely on insight and the synthesis of a variety of mathematical ideas.

This text aims to provide graduate students with a self-contained introduction to topics that are at the forefront of modern algebra, namely, coalgebras, bialgebras and Hopf algebras.

The main results of this book combine pseudo differential analysis with modular form theory.

The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory.

Analysis, assessment, and data management are core competencies for operation research analysts.

This volume develops the depth and breadth of the mathematics underlying the construction and analysis of Hadamard matrices, and their use in the construction of combinatorial designs.

This book is the English translation of Baumgart's thesis on the early proofs of the quadratic reciprocity law ("e;Uber das quadratische Reciprocitatsgesetz.

This innovative textbook introduces a new pattern-based approach to learning proof methods in the mathematical sciences.

Focusing on an approach of solving rigorous problems and learning how to prove, this volume is concentrated on two specific content themes, elementary number theory and algebraic polynomials.

This collection of surveys and research articles explores a fascinating class of varieties: Beauville surfaces.

The new theory of Jacobi forms over totally real number fields introduced in this monograph is expected to give further insight into the arithmetic theory of Hilbert modular forms, its L-series, and into elliptic curves over number fields.

The text presents the birational classification of holomorphic foliations of surfaces.

The techniques presented here are useful for solving mathematical contest problems in algebra and analysis.

This edited volume presents a collection of carefully refereed articles covering the latest advances in Automorphic Forms and Number Theory, that were primarily developed from presentations given at the 2012 "e;International Conference on Automorphic Forms and Number Theory,"e; held in Muscat, Sultanate of Oman.

This book gives a comprehensive treatment of random phenomena and distribution results in diophantine approximation, with a particular emphasis on quadratic irrationals.

This volume of papers presented at the conference in honor of Calixto P.

In 1842 the Belgian mathematician Eugene Charles Catalan asked whether 8 and 9 are the only consecutive pure powers of non-zero integers.

The Lie Theory Workshop, founded by Joe Wolf (UC, Berkeley), has been running for over two decades.

The Lie Theory Workshop, founded by Joe Wolf (UC, Berkeley), has been running for over two decades.

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The primary intent of the book is to introduce an array of beautiful problems in a variety of subjects quickly, pithily and completely rigorously to graduate students and advanced undergraduates.

This undergraduate textbook provides an approachable and thorough introduction to the topic of algebraic number theory, taking the reader from unique factorisation in the integers through to the modern-day number field sieve.

Designed for an undergraduate course or for independent study, this text presents sophisticated mathematical ideas in an elementary and friendly fashion.

Analysis, assessment, and data management are core competencies for operation research analysts.

This is the first work on Discrepancy Theory to show the present variety of points of view and applications covering the areas Classical and Geometric Discrepancy Theory, Combinatorial Discrepancy Theory and Applications and Constructions.

This short monograph is the first book to focus exclusively on the study of summability methods, which have become active areas of research in recent years.

The aim of this work is to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud.

These notes introduce a new class of algebraic curves on Hilbert modular surfaces.

This volume contains original research articles, survey articles and lecture notes related to the Computations with Modular Forms 2011 Summer School and Conference, held at the University of Heidelberg.