Number theory Books

Important results on the Hilbert modular group and Hilbert modular forms are introduced and described in this book. In recent times, this branch of number theory has been given more and more attention and thus the need for a...

Einführung in die Grundgedanken der modernen algebraischen Zahlentheorie, einer der traditionsreichsten und besonders aktuellen Grunddisziplinen der Mathematik. Ausgehend von Themen, die üblicherweise der elementaren...

This book constitutes the refereed proceedings of the Third International Workshop on Ant Algorithms, ANTS 2002, held in Brussels, Belgium in September 2002.The 17 revised full papers, 11 short papers, and extended poster...

Around 1994 R. Borcherds discovered a new type of meromorphic modular form on the orthogonal group $O(2,n)$. These "Borcherds products" have infinite product expansions analogous to the Dedekind eta-function. They arise as...

This volume of proceedings is an offspring of the special semester Ergodic Theory, Geometric Rigidity and Number Theory which was held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK, from Jan­ uary...

This book gives an account of theoretical and algorithmic developments on the integral closure of algebraic structures. It gives a comprehensive treatment of Rees algebras and multiplicity theory while pointing to applications...

Provides a wide range of mathematical models currently used in the life sciences Each model is thoroughly explained and illustrated by example Includes three appendices to allow for independent reading

This volume deals with various topics around equivariant holomorphic maps of Hermitian symmetric domains and is intended for specialists in number theory and algebraic geometry. In particular, it contains a...

Heegner points on both modular curves and elliptic curves over global fields of any characteristic form the topic of this research monograph. The Heegner module of an elliptic curve is an original concept introduced in...

Tauberian theory compares summability methods for series and integrals, helps to decide when there is convergence, and provides asymptotic and remainder estimates. The author shows the development of the theory from the...

Since its publication, C.F. Gauss's Disquisitiones Arithmeticae (1801) has acquired an almost mythical reputation, standing as an ideal of exposition in notation, problems and methods; as a model of organisation and theory...

This edition has been called 'startlingly up-to-date', and in this corrected second printing you can be sure that it's even more contemporaneous. It surveys from a unified point of view both the modern state and the trends of...

This volume contains proceedings of two conferences held in Toronto (Canada) and Kozhikode (India) in 2016 in honor of the 60th birthday of Professor Kumar Murty. The meetings were focused on several aspects of number theory: The ...

This volume brings together recent, original research and survey articles by leading experts in several fields that include singularity theory, algebraic geometry and commutative algebra. The motivation for this collection comes from the wide-ranging...

This book discusses the mathematical interests of Joachim Schwermer, who throughout his career has focused on the cohomology of arithmetic groups, automorphic forms and the geometry of arithmetic manifolds. To mark his 66th birthday, the editors brought...

The contributions in this book explore various contexts in which the derived category of coherent sheaves on a variety determines some of its arithmetic. This setting provides new geometric tools for interpreting elements of the Brauer group. With a view...

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. Emphasis is also given to problems in interdisciplinary research for...

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...

This book presents a collection of carefully refereed research articles and lecture notes stemming from the Conference "Automorphic Forms and L-Functions", held at the University of Heidelberg in 2016. The theory of automorphic forms and their associated...

This book provides the first extensive survey of block ciphers following the Lai-Massey design paradigm. After the introduction, with historical remarks, the author structures the book into a chapter on the description of the PES, IDEA and other related...

This book provides the latest competing research results on non-commutative harmonic analysis on homogeneous spaces with many applications. It also includes the most recent developments on other areas of mathematics including algebra and geometry.Lie...

Exploring the Riemann Zeta Function: 190 years from Riemann's Birth presents a collection of chapters contributed by eminent experts devoted to the Riemann Zeta Function, its generalizations, and their various applications to several scientific...

This book contains selected papers based on talks given at the "Representation Theory, Number Theory, and Invariant Theory" conference held at Yale University from June 1 to June 5, 2015. The meeting and this resulting volume are in honor of Professor...

This unique book explores the world of q, known technically as basic hypergeometric series, and represents the author's personal and life-long study-inspired by Ramanujan-of aspects of this broad topic. While the level of mathematical sophistication is...

This volume of papers presented at the conference in honor of Calixto P. Calderón by his friends, colleagues, and students is intended to make the mathematical community aware of his important scholarly and research contributions in contemporary Harmonic...

Covering topics in graph theory, L-functions, p-adic geometry, Galois representations, elliptic fibrations, genus 3 curves and bad reduction, harmonic analysis, symplectic groups and mould combinatorics, this volume presents a collection of papers...

Ce travail en deux volumes donne la preuve de la stabilisation de la formule des trace tordue.Stabiliser la formule des traces tordue est la méthode la plus puissante connue actuellement pour comprendre l'action naturelle du groupe des points adéliques...

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...

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. Ranging from the...

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. At the same time, it pursues current research in their numerous...

This book is the English translation of Baumgart's thesis on the early proofs of the quadratic reciprocity law ("Über das quadratische Reciprocitätsgesetz. Eine vergleichende Darstellung der Beweise"), first published in 1885. It is divided into two...

This volume contains 21 research and survey papers on recent developments in the field of diophantine approximation, which are based on lectures given at a conference at the Erwin Schrödinger-Institute (Vienna, 2003). The...

It would be difficult to overestimate the influence and importance of modular forms, modular curves, and modular abelian varieties in the development of num­ ber theory and arithmetic geometry during the last fifty years. These...

At the heart of Clifford analysis is the study of systems of special partial differential operators that arise naturally from the use of Clifford algebra as a calculus tool. This book focuses on the study of Dirac operators and...

Abelian varieties and their moduli are a topic of increasing importance in today`s mathematics, applications ranging from algebraic geometry and number theory to mathematical physics. This collection of 17 refereed articles...

This volume began as the last part of a one-term graduate course given at the Fields Institute for Research in the Mathematical Sciences in the Autumn of 1993. The course was one of four associated with the 1993-94 Fields...

To mark the World Mathematical Year 2000 an International Conference on Number Theory and Discrete Mathematics in honour of the legendary Indian Mathematician Srinivasa Ramanuj~ was held at the centre for Advanced study in...

The book introduces new techniques that imply rigorous lower bounds on the com­ plexity of some number-theoretic and cryptographic problems. It also establishes certain attractive pseudorandom properties of various ...

This book contains survey papers based on the lectures presented at the 3rd International Winter School "Modern Problems of Mathematics and Mechanics" held in January 2010 at the Belarusian State University, Minsk. These lectures are devoted to different...

This volume consists of the English translations of the letters exchanged between Emil Artin to Helmut Hasse written from 1921 until 1958. The letters are accompanied by extensive comments explaining the mathematical background and giving the information...

Quaternion and Clifford Fourier and wavelet transformations generalize the classical theory to higher dimensions and are becoming increasingly important in diverse areas of mathematics, physics, computer science and engineering. This edited volume...

To date, the theoretical development of q-calculus has rested on a non-uniform basis. Generally, the bulky Gasper-Rahman notation was used, but the published works on q-calculus looked different depending on where and by whom they were written. This...

Although the Lucas sequences were known to earlier investigators such as Lagrange, Legendre and Genocchi, it is because of the enormous number and variety of results involving them, revealed by Édouard Lucas between 1876 and 1880, that they are now named...

This monograph describes and implements partially homomorphic encryption functions using a unified notation. After introducing the appropriate mathematical background, the authors offer a systematic examination of the following known algorithms:...

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 positivity for a real polynomial is an algebraic identity that...

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. Although the event, originally...

This monograph provides a systematic treatment of the Brauer group of schemes, from the foundational work of Grothendieck to recent applications in arithmetic and algebraic geometry. The importance of the cohomological Brauer group for applications to...