Number theory

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.

A series of three symposia took place on the topic of trace formulas, each with an accompanying proceedings volume.

This book gives its readers a unique opportunity to get acquainted with new aspects of the fruitful interactions between Analysis, Geometry, Quantum Mechanics and Number Theory.

This is the fourth in a series of proceedings of the Combinatorial and Additive Number Theory (CANT) conferences, based on talks from the 2019 and 2020 workshops at the City University of New York.

This volume introduces some recent developments in Arithmetic Geometry over local fields.

This book is an outgrowth of the conference "e;Regulators IV: An International Conference on Arithmetic L-functions and Differential Geometric Methods"e; that was held in Paris in May 2016.

This textbook is a practical yet in depth guide to cryptography and its principles and practices.

This edited volume presents state-of-the-art developments in various areas in which Harmonic Analysis is applied.

This volume explores the rich interplay between number theory and wireless communications, reviewing the surprisingly deep connections between these fields and presenting new research directions to inspire future research.

This monograph provides a self-contained presentation of the foundations of finite fields, including a detailed treatment of their algebraic closures.

In this book, the author pays tribute to Bernhard Riemann (1826-1866), a mathematician with revolutionary ideas, whose work on the theory of integration, the Fourier transform, the hypergeometric differential equation, etc.

This book gathers nineteen papers presented at the first NLAGA-BIRS Symposium, which was held at the Cheikh Anta Diop University in Dakar, Senegal, on June 24-28, 2019.

This book presents a printed testimony for the fact that George Andrews, one of the world's leading experts in partitions and q-series for the last several decades, has passed the milestone age of 80.

This textbook covers a wide array of topics in analytic and multiplicative number theory, suitable for graduate level courses.

This textbook explores a selection of topics in complex analysis.

This book takes the reader on a journey from familiar high school mathematics to undergraduate algebra and number theory.

This textbook provides a unified and concise exploration of undergraduate mathematics by approaching the subject through its history.

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.

This book presents original peer-reviewed contributions from the London Mathematical Society (LMS) Midlands Regional Meeting and Workshop on 'Galois Covers, Grothendieck-Teichmuller Theory and Dessinsd'Enfants', which took place at the University of Leicester, UK, from 4 to 7 June, 2018.

This textbook introduces exciting new developments and cutting-edge results on the theme of hyperbolicity.

There are numbers of all kinds: rational, real, complex, p-adic, and more.

This book discusses regular powers and symbolic powers of ideals from three perspectives- algebra, combinatorics and geometry - and examines the interactions between them.

This graduate textbook offers an introduction to modern methods in number theory.

This proceedings volume contains articles related to the research presented at the 2017 Simons Symposium on p-adic Hodge theory.

This textbook provides a rigorous analytical treatment of the theory of Maass wave forms.

This book presents the state of the art on numerical semigroups and related subjects, offering different perspectives on research in the field and including results and examples that are very difficult to find in a structured exposition elsewhere.

This book is the outcome of research initiatives formed during the special ``Research Trimester on Multiple Zeta Values, Multiple Polylogarithms, and Quantum Field Theory' at the ICMAT (Instituto de Ciencias Matematicas, Madrid) in 2014.

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.

This book gathers together selected contributions presented at the 3rd Moroccan Andalusian Meeting on Algebras and their Applications, held in Chefchaouen, Morocco, April 12-14, 2018, and which reflects the mathematical collaboration between south European and north African countries, mainly France, Spain, Morocco, Tunisia and Senegal.

Based on talks from the 2017 and 2018 Combinatorial and Additive Number Theory (CANT) workshops at the City University of New York, these proceedings offer 17 peer-reviewed and edited papers on current topics in number theory.

This textbook introduces exciting new developments and cutting-edge results on the theme of hyperbolicity.

This authoritative volume in honor of  Alain Connes, the foremost architect of Noncommutative Geometry, presents the state-of-the art in the subject.

This book explores various properties of quasimodular forms, especially their connections with Jacobi-like forms and automorphic pseudodifferential operators.

This monograph outlines the structure of index form equations, and makes clear their relationship to other classical types of Diophantine equations.

These proceedings collect several number theory articles, most of which were written in connection to the workshop WIN4: Women in Numbers, held in August 2017, at the Banff International Research Station (BIRS) in Banff, Alberta, Canada.

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 on the symplectic group.

This volume collects lecture notes and research articles from the International Autumn School on Computational Number Theory, which was held at the Izmir Institute of Technology from October 30th to November 3rd, 2017 in Izmir, Turkey.

This book is the outcome of research initiatives formed during the special ``Research Trimester on Multiple Zeta Values, Multiple Polylogarithms, and Quantum Field Theory' at the ICMAT (Instituto de Ciencias Matematicas, Madrid) in 2014.

The most recent methods in various branches of lattice path and enumerative combinatorics along with relevant applications are nicely grouped together and represented in this research contributed volume.

This book develops a novel approach to perturbative quantum field theory: starting with a perturbative formulation of classical field theory, quantization is achieved by means of deformation quantization of the underlying free theory and by applying the principle that as much of the classical structure as possible should be maintained.

The book is aimed at people working in number theory or at least interested in this part of mathematics.

Right triangles are at the heart of this textbook's vibrant new approach to elementary number theory.

This book contains a multitude of challenging problems and solutions that are not commonly found in classical textbooks.

The objective of this book is to provide tools for solving problems which involve cubic number fields.

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 continuation and functional equation of automorphic L-functions.

This is the first extensive biography of the influential German mathematician, Peter Gustav Lejeune Dirichlet (1805 - 1859).

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

The most recent methods in various branches of lattice path and enumerative combinatorics along with relevant applications are nicely grouped together and represented in this research contributed volume.

A new approach to the character theory of the symmetric group has been developed during the past fifteen years which is in many ways more efficient, more transparent, and more elementary.