Number Theory 20

This textbook offers a unique introduction to classical Galois theory through many concrete examples and exercises of varying difficulty (including computer-assisted exercises). In addition to cover……続きを見る

Requiring no more than a basic knowledge of abstract algebra, this textbook presents the basics of algebraic number theory in a straightforward, "down-to-earth" manner. It thus avoids local methods,……続きを見る

This textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and ei……続きを見る

This text introduces cryptography, from its earliest roots to cryptosystems used today for secure online communication. Beginning with classical ciphers and their cryptanalysis, this book proceeds t……続きを見る

This book contains a multitude of challenging problems and solutions that are not commonly found in classical textbooks. One goal of the book is to present these fascinating mathematical problems in……続きを見る

Presenting the first systematic treatment of the behavior of Néron models under ramified base change, this book can be read as an introduction to various subtle invariants and constructions related ……続きを見る

This monograph introduces two approaches to studying Siegel modular forms: the classical approach as holomorphic functions on the Siegel upper half space, and the approach via representation theory ……続きを見る

The main topics of this volume, dedicated to Lance Littlejohn, are operator and spectral theory, orthogonal polynomials, combinatorics, number theory, and the various interplays of these subjects. A……続きを見る

This book collects and explains the many theorems concerning the existence of certificates of positivity for polynomials that are positive globally or on semialgebraic sets. A certificate of positiv……続きを見る

Mahler measure, a height function for polynomials, is the central theme of this book. It has many interesting properties, obtained by algebraic, analytic and combinatorial methods. It is the subject……続きを見る

This graduate textbook offers an introduction to modern methods in number theory. It gives a complete account of the main results of class field theory as well as the Poitou-Tate duality theorems, c……続きを見る

This book focuses on a conjectural class of zeta integrals which arose from a program born in the work of Braverman and Kazhdan around the year 2000, the eventual goal being to prove the analytic co……続きを見る

The aim of this book is to provide a comprehensive account of higher dimensional Nevanlinna theory and its relations with Diophantine approximation theory for graduate students and interested resear……続きを見る

This problem book gathers together 15 problem sets on analytic number theory that can be profitably approached by anyone from advanced high school students to those pursuing graduate studies. It eme……続きを見る

This volume contains the notes originally made by Kenkichi Iwasawa in his own handwriting for his lecture course at Princeton University in 1964. These notes give a beautiful and completely detailed……続きを見る

This volume presents a lively introduction to the rapidly developing and vast research areas surrounding Calabi–Yau varieties and string theory. With its coverage of the various perspectives of a wi……続きを見る

The Hardy–Littlewood circle method was invented over a century ago to study integer solutions to special Diophantine equations, but it has since proven to be one of the most successful all-purpose t……続きを見る

This book, the first of two volumes, contains over 250 selected exercises in Algebra which have featured as exam questions for the Arithmetic course taught by the authors at the University of Pisa. ……続きを見る

This textbook offers a rigorous presentation of mathematics before the advent of calculus. Fundamental concepts in algebra, geometry, and number theory are developed from the foundations of set theo……続きを見る

This book aims to provide an introduction to the broad and dynamic subject of discrete energy problems and point configurations. Written by leading authorities on the topic, this treatise is designe……続きを見る

This undergraduate textbook provides an elegant introduction to the arithmetic of quadratic number fields, including many topics not usually covered in books at this level. Quadratic fields offer an……続きを見る

This book discusses regular powers and symbolic powers of ideals from three perspectives– algebra, combinatorics and geometry – and examines the interactions between them. It invites readers to expl……続きを見る

These notes introduce a new class of algebraic curves on Hilbert modular surfaces. These curves are called twisted Teichmüller curves, because their construction is very reminiscent of Hirzebruch-Za……続きを見る

The section conjecture in anabelian geometry, announced by Grothendieck in 1983, is concerned with a description of the set of rational points of a hyperbolic algebraic curve over a number field in ……続きを見る

This edited volume presents state-of-the-art developments in various areas in which Harmonic Analysis is applied. Contributions cover a variety of different topics and problems treated such as struc……続きを見る

This book is a history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted to complex ……続きを見る

This self-contained text presents state-of-the-art results on recurrent sequences and their applications in algebra, number theory, geometry of the complex plane and discrete mathematics. It is desi……続きを見る

This textbook provides a rigorous analytical treatment of the theory of Maass wave forms. Readers will find this unified presentation invaluable, as it treats Maass wave forms as the central area of……続きを見る

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 mod……続きを見る

This book provides an introduction to state-of-the-art applications of homotopy theory to arithmetic geometry. The contributions to this volume are based on original lectures by leading researchers ……続きを見る