Number theory

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

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

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

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 volume includes articles spanning several research areas in number theory, such as arithmetic geometry, algebraic number theory, analytic number theory, and applications in cryptography and coding theory.

This proceedings volume gathers selected, peer-reviewed papers presented at the 2nd International Conference on Mathematics and its Applications in Science and Engineering - ICMASE 2021, which was virtually held on July 1-2, 2021 by the University of Salamanca, Spain.

This book develops a new theory in convex geometry, generalizing positive bases and related to Caratheordory's Theorem by combining convex geometry, the combinatorics of infinite subsets of lattice points, and the arithmetic of transfer Krull monoids (the latter broadly generalizing the ubiquitous class of Krull domains in commutative algebra)This new theory is developed in a self-contained way with the main motivation of its later applications regarding factorization.

This book concentrates on the modern theory of dynamical systems and its interactions with number theory and combinatorics.

This book presents a method for evaluating Selberg zeta functions via transfer operators for the full modular group and its congruence subgroups with characters.

This volume is dedicated to Robert F.

This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory.

This textbook offers a unique exploration of analytic number theory that is focused on explicit and realistic numerical bounds.

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 disciplines, including Analytic Number Theory, Harmonic Analysis, Complex Analysis, Probability Theory, and related subjects.

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.

Inspired by the September 2016 conference of the same name, this second volume highlights recent research in a wide range of topics in contemporary number theory and arithmetic geometry.

This book provides an introduction to state-of-the-art applications of homotopy theory to arithmetic geometry.

This book develops the foundations of "e;summability calculus"e;, which is a comprehensive theory of fractional finite sums.

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.

Requiring no more than a basic knowledge of abstract algebra, this textbook presents the basics of algebraic number theory in a straightforward, "e;down-to-earth"e; manner.

This volume features contributions from the Women in Commutative Algebra (WICA) workshop held at the Banff International Research Station (BIRS) from October 20-25, 2019, run by the Pacific Institute of Mathematical Sciences (PIMS).

Through its engaging and unusual problems, this book demonstrates methods of reasoning necessary for learning number theory.

Mahler measure, a height function for polynomials, is the central theme of this book.

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

This contributed volume provides readers with an overview of the most recent developments in the mathematical fields related to fractals, including both original research contributions, as well as surveys from many of the leading experts on modern fractal theory and applications.

This volume presents the revised papers of the 14th International Conference in Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2020, which took place online during August 10-14, 2020.

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 textbook offers a unique introduction to classical Galois theory through many concrete examples and exercises of varying difficulty (including computer-assisted exercises).

Many different fractal dimensions have been proposed for networks.

This unique collection of new and classical problems provides full coverage of algebraic inequalities.

This book presents a collection of carefully refereed research articles and lecture notes stemming from the Conference "e;Automorphic Forms and L-Functions"e;, held at the University of Heidelberg in 2016.

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.

This highly readable book aims to ease the many challenges of starting undergraduate research.

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

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.

This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 "e;Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory"e;, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016.

The aim of this monograph is to give a detailed exposition of the summation method that Ramanujan uses in Chapter VI of his second Notebook.

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

This book provides an overview of many interesting properties of natural numbers, demonstrating their applications in areas such as cryptography, geometry, astronomy, mechanics, computer science, and recreational mathematics.

Kenntnisse über den Aufbau des Zahlensystems und über elementare zahlentheoretische Prinzipien gehören zum unverzichtbaren Grundwissen in der Mathematik.

This text introduces cryptography, from its earliest roots to cryptosystems used today for secure online communication.

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.

Dieses Kryptographiebuch ist geschrieben für Studierende der Mathematik, Informatik, Physik, Elektrotechnik oder andere Leser mit mathematischer Grundbildung und wurde in vielen Vorlesungen erfolgreich eingesetzt.

The second of three volumes devoted to the study of the trace formula, these proceedings focus on automorphic representations of higher rank groups.

This book includes a self-contained approach of the general theory of quadratic forms and integral Euclidean lattices, as well as a presentation of the theory of automorphic forms and Langlands' conjectures, ranging from the first definitions to the recent and deep classification results due to James Arthur.

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 eighteenth centuries, and exploring the impact of ideas on the development of the subject.

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

This book offers an organized and systematic approach to poset metrics and codes.