Number Theory

The main topic of this book is the deep relation between the spacings between zeros of zeta and $L$-functions and spacings between eigenvalues of random elements of large compact classical groups. The authors draw upon many disparate areas of mathematics...

A publication of the University of Michigan's Science Series, The Asymptotic Developments of Functions Defined by Maclaurin Series by Walter Burton Ford is an inquiry into the problem of functions defined by Maclaurin series. Here, Ford introduces his...

A comprehensive new theory of adelic line bundles on quasi-projective varieties over finitely generated fieldsThis book introduces a comprehensive theory of adelic line bundles on quasi-projective varieties over finitely generated fields, developed in...

This is an open access volume and it containscontains several number theory contributions, most of which were written in connection to the workshop WIN6: Women in Numbers, held in March 2023, at the Banff International Research Station (BIRS) in Banff,...

The Budapest semesters in mathematics were initiated with the aim of offering undergraduate courses that convey the tradition of Hungarian mathematics to English-speaking students.This book is an elaborate version of the course on Conjecture and Proof...

In mathematics, technical difficulties can spark groundbreaking ideas. This book explores one such challenge: a problem that arose in the formative years of algebraic number theory and played a major role in the early development of the field. When...

"Who would have thought a book on random numbers would be more than randomly interesting? Author Szpiro draws readers in with clarity, wit and readily understood examples. Plenty of history, examples and some solid math for the cognoscenti!"-Vint Cerf,...

Why are there more poor people with small bank accounts than rich people with big bank accounts? Why are there more small planets and stars than big ones in the cosmos? And why are there more small rivers than big rivers, and more harmless tremors than...

Written for advanced undergraduate and first-year graduate students, this book aims to introduce students to a serious level of p-adic analysis with important implications for number theory. The main object is the study of G-series, that is, power series...

An examination of some of the remarkable connections between group theory and arithmetic algebraic geometry over finite fieldsExponential sums have been of great interest ever since Gauss, and their importance in analytic number theory goes back a...

Apologies but we at Booksplease don't have a full description for this book.About the AuthorMathias Petreolle, University College London, United Kingdom.Alan D. Sokal, University College London, United Kingdom, and New York University, New York.Bao-Xuan...

Convolution and Equidistribution explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view. The book presents fundamentally important results and a...

Codes on Euclidean spheres are often referred to as spherical codes. They are of interest from mathematical, physical and engineering points of view. Mathematically the topic belongs to the realm of algebraic combinatorics, with close connections to...

The book is directed toward students with a minimal background who want to learn class field theory for number fields. The only prerequisite for reading it is some elementary Galois theory. The first three chapters lay out the necessary background in...

The key feature at this conference was the 33 invited papers from the world's leading number theorists. Talks were in three sessions: analytical number theory; arithmetical algebraic geometry; and diophantive approximation. Speakers included: F.Beukers...

The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the...

This volume is dedicated to Robert F. Tichy on the occasion of his 60th birthday. Presenting 22 research and survey papers written by leading experts in their respective fields, it focuses on areas that align with Tichy's research interests and which he...

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...

Two major subjects are treated in this book. The main one is the theory of Bernoulli numbers and the other is the theory of zeta functions. Historically, Bernoulli numbers were introduced to give formulas for the sums of powers of consecutive integers...

For the most part, this book is the translation from Japanese of the earlier book written jointly by Koji Doi and the author who revised it substantially for the English edition. It sets out to provide the reader with the basic knowledge of elliptic...

Sorry no description is available for this book at this time.

The study of geometric discrepancy, which provides a framework for quantifying the quality of a distribution of a finite set of points, has experienced significant growth in recent decades. This book provides a self-contained course in number theory,...

For a long time - at least from Fermat to Minkowski - the theory of quadratic forms was a part of number theory. Much of the best work of the great number theorists of the eighteenth and nineteenth century was concerned with problems about quadratic...

The contents of this book was created by the authors as a simultaneous generalization of Witten zeta-functions, Mordell-Tornheim multiple zeta-functions, and Euler-Zagier multiple zeta-functions. Zeta-functions of root systems are defined by certain...

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...

The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the...

This is the proceedings of the conference 'Primitive Forms and Related Subjects' held at Kavli IPMU, the University of Tokyo in February 10-14, 2014. The principal aim of the conference was to discuss the current status of rapidly developing subjects...

Quantum computers will break today's most popular public-key cryptographic systems, including RSA, DSA, and ECDSA. This book introduces the reader to the next generation of cryptographic algorithms, the systems that resist quantum-computer attacks: in...

Srinivasa Ramanujan was a mathematician brilliant beyond comparison who inspired many great mathematicians. There is extensive literature available on the work of Ramanujan. But what is missing in the literature is an analysis that would place his...

This book casts the theory of periods of algebraic varieties in the natural setting of Madhav Nori's abelian category of mixed motives. It develops Nori's approach to mixed motives from scratch, thereby filling an important gap in the literature, and...

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...

This contributed volume presents recent advances as well as new directions in number theory and its applications. Algebraic and analytic number theory are the main focus with chapters showing how these areas are rapidly evolving. By gathering authors...

The book is aimed at people working in number theory or at least interested in this part of mathematics. It presents the development of the theory of algebraic numbers up to the year 1950 and contains a rather complete bibliography of that period. The...

The second of two volumes presenting papers from an international conference on analytic number theory. The two volumes contain 50 papers, with an emphasis on topics such as sieves, related combinatorial aspects, multiplicative number theory, additive...

[Hilbert's] style has not the terseness of many of our modem authors in mathematics, which is based on the assumption that printer's labor and paper are costly but the reader's effort and time are not. H. Weyl [143] The purpose of this book is to...

The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory. This text adopts the latter perspective by applying an arithmetic-algebraic viewpoint to the study of...

The last one hundred years have seen many important achievements in the classical part of number theory. After the proof of the Prime Number Theorem in 1896, a quick development of analytical tools led to the invention of various new methods, like Brun's...

One of the great successes of twentieth century mathematics has been the remarkable qualitative understanding of rational and integral points on curves, gleaned in part through the theorems of Mordell, Weil, Siegel, and Faltings. It has become clear that...

Peter L. Montgomery has made significant contributions to computational number theory, introducing many basic tools such as Montgomery multiplication, Montgomery simultaneous inversion, Montgomery curves, and the Montgomery ladder. This book features...

With this translation, the classic monograph UEber die Klassenzahl abelscher Zahlkoerper by Helmut Hasse is now available in English for the first time.The book addresses three main topics: class number formulas for abelian number fields; expressions of...