Number theory

Alexander Grothendieck is often considered one of the greatest mathematicians of the twentieth century (if not all time), and his unique vision continues to impact and inspire many fields and researchers today.

This volume contains three long lecture series by J.

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.

This volume provides readers with an overview of the most recent developments in the mathematical fields related to fractals.

This book constitutes the refereed post-conference proceedings of the 4th International Conference on Number-Theoretic Methods in Cryptology, NuTMiC 2024, held in Szczecin, Poland, during June 24–26, 2024.

This self-contained and comprehensive textbook of algebraic number theory is useful for advanced undergraduate and graduate students of mathematics.

A large number of comprehensive publications has been devoted to the Antarctic, to its plant and animal life.

This volume presents modern trends in the area of symmetries and their applications based on contributions from the workshop "e;Lie Theory and Its Applications in Physics"e;, held near Varna, Bulgaria, in June 2015.

This monograph explores the finiteness and structure of Shafarevich-Tate groups of abelian varieties over global fields of any characteristic.

This book is the first volume of proceedings from the joint conference X International Symposium "e;Quantum Theory and Symmetries"e; (QTS-X) and XII International Workshop "e;Lie Theory and Its Applications in Physics"e; (LT-XII), held on 19-25 June 2017 in Varna, Bulgaria.

In this volume we present a survey of the theory of Galois module structure for rings of algebraic integers.

Cyclotomic fields have always occupied a central place in number theory, and the so called "e;main conjecture"e; on cyclotomic fields is arguably the deepest and most beautiful theorem known about them.

In mathematics we are interested in why a particular formula is true.

The starting point of this Lecture Notes volume is Deligne's theorem about absolute Hodge cycles on abelian varieties.

Absolute values and their completions -like the p-adic number fields- play an important role in number theory.

It is gratifying that this textbook is still sufficiently popular to warrant a third edition.

"e;This book by a leading researcher and masterly expositor of the subject studies diophantine approximations to algebraic numbers and their applications to diophantine equations.

This English translation of Karatsuba's Basic Analytic Number Theory follows closely the second Russian edition, published in Moscow in 1983.

These proceedings include selected and refereed original papers; most are research papers, a few are comprehensive survey articles.

Number theory is a branch of mathematics which draws its vitality from a rich historical background.

Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics.

This book is concerned with discontinuous groups of motions of the unique connected and simply connected Riemannian 3-manifold of constant curva- ture -1, which is traditionally called hyperbolic 3-space.

This book serves as an illuminating introduction to the intricacies of the geometry of numbers.

From its birth (in Babylon?

This textbook invites readers to explore mathematical thinking by finding the beauty in the subject.

It was the aim of the Erlangen meeting in May 1988 to bring together number theoretists and algebraic geometers to discuss problems of common interest, such as moduli problems, complex tori, integral points, rationality questions, automorphic forms.

On the one hand, this monograph serves as a self-contained introduction to Nevanlinna's theory of value distribution because the authors only assume the reader is familiar with the basics of complex analysis.

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind.

Integral Closure gives an account of theoretical and algorithmic developments on the integral closure of algebraic structures.

This book systematically develops the theory of continuous representations on p-adic Banach spaces.

This book describes a novel approach to the study of Siegel modular forms of degree two with paramodular level.

This introductory text is designed for undergraduate courses in number theory, covering both elementary number theory and analytic number theory.

The last one hundred years have seen many important achievements in the classical part of number theory.

In the English edition, the chapter on the Geometry of Numbers has been enlarged to include the important findings of H.

This introductory text is designed for undergraduate courses in number theory, covering both elementary number theory and analytic number theory.

This volume is an English translation of "e;Cohomologie Galoisienne"e; .

This book delves into the dynamic intersection of optimization and discrete mathematics, offering a comprehensive exploration of their applications in data sciences.

Although this is an introductory text on proof theory, most of its contents is not found in a unified form elsewhere in the literature, except at a very advanced level.

The problem of uniform distribution of sequences initiated by Hardy, Little- wood and Weyl in the 1910's has now become an important part of number theory.

Many people do not realise that mathematics provides the foundation for the devices we use to handle information in the modern world.