Number theory

Provides a novel interdisciplinary perspective on the state of the art of ultrametric pseudodifferential equations and their applications.

Our grasp of numbers and uncertainty is one of humankind's most distinctive and important traits.

From the reviews:"e;The book.

To many laymen, mathematicians appear to be problem solvers, people who do "e;hard sums"e;.

This is the second of three volumes devoted to elementary finite p-group theory.

The famous problems of squaring the circle, doubling the cube and trisecting an angle captured the imagination of both professional and amateur mathematicians for over two thousand years.

The algebraic techniques developed by Kakde will almost certainly lead eventually to major progress in the study of congruences between automorphic forms and the main conjectures of non-commutative Iwasawa theory for many motives.

The book is an introduction to the theory of cubic metaplectic forms on the 3-dimensional hyperbolic space and the author's research on cubic metaplectic forms on special linear and symplectic groups of rank 2.

The Primality Testing Problem (PTP) has now proved to be solvable in deterministic polynomial-time (P) by the AKS (Agrawal-Kayal-Saxena) algorithm, whereas the Integer Factorization Problem (IFP) still remains unsolvable in (P).

This book provides the first extensive survey of block ciphers following the Lai-Massey design paradigm.

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

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

Written by experts in both mathematics and biology, Algebraic and Discrete Mathematical Methods for Modern Biology offers a bridge between math and biology, providing a framework for simulating, analyzing, predicting, and modulating the behavior of complex biological systems.

A Mathematical Tour introduces readers to a selection of mathematical topics chosen for their centrality, importance, historical significance, and intrinsic appeal and beauty.

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.

Now the most used texbook for introductory cryptography courses in both mathematics and computer science, the Third Edition builds upon previous editions by offering several new sections, topics, and exercises.

Presenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; 2) undecidability in arithmetic; 3) NIP theories; and 4) the model theory of real and complex exponentiation.

The notes in this volume correspond to advanced courses held at the Centre de Recerca Matematica as part of the research program in Arithmetic Geometry in the 2009-2010 academic year.

A self-contained 2010 account of the state of the art in classical complex multiplication.

Elliptic cohomology is an extremely beautiful theory with both geometric and arithmetic aspects.

This book is a revised and greatly expanded version of our book Elements of Number Theory published in 1972.

A look at one of the most exciting unsolved problems in mathematics todayElliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics-the Birch and Swinnerton-Dyer Conjecture.

Research in mathematics is much more than solving puzzles, but most people will agree that solving puzzles is not just fun: it helps focus the mind and increases one's armory of techniques for doing mathematics.

In this monograph p-adic period domains are associated to arbitrary reductive groups.

System Theory

Number theory is one of the oldest branches of mathematics that is primarily concerned with positive integers.

The subject of this book is probabilistic number theory.

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

About the bookIn honor of Edgar Enochs and his venerable contributions to a broad range of topics in Algebra, top researchers from around the world gathered at Auburn University to report on their latest work and exchange ideas on some of today's foremost research topics.

"e;Modular Forms with Integral and Half-Integral Weights"e; focuses on the fundamental theory of modular forms of one variable with integral and half-integral weights.

This book is designed for a topics course in computational number theory.

Graduate text covering the theory of Hardy spaces from its origins to the present, with concrete applications and solved exercises.

Since 1973, Galois theory has been educating undergraduate students on Galois groups and classical Galois theory.

Eine kombinierte Einführung in die Algebra bis zur Galoistheorie und ihren klassischen Anwendungen sowie in die Zahlentheorie.

Originally published in 1994, The Incommensurability Thesis is a critical study of the Incommensurability Thesis of Thomas Kuhn and Paul Feyerabend.

A central concern of number theory is the study of local-to-global principles, which describe the behavior of a global field K in terms of the behavior of various completions of K.

The world''s leading authorities describe the state of the art in Serre''s conjecture and rational points on algebraic varieties.

In this book, the author writes freely and often humorously about his life, beginning with his earliest childhood days.

In the 20th century, many mathematicians in Russia made great contributions to the field of mathematics.

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.

This monograph provides a brief exposition of automorphic forms of weight 1 and their applications to arithmetic, especially to Galois representations.