Introduction to Arithmetic Theory of Automorphic Functions

This book collects more than thirty contributions in memory of Wolfgang Schwarz, most of which were presented at the seventh International Conference on Elementary and Analytic Number Theory (ELAZ), h

Concise treatment covers basics of Fuchsian groups, development of Poincare series and automorphic forms, and the connection between theory of Riemann surfaces with theories of automorphic forms and d

This book is designed both for FPGA users interested in developing new, specific components - generally for reducing execution times –and IP core designers interested in extending their catalog of spe

Multiple Dirichlet Series, L-functions and Automorphic Forms gives the latest advances in the rapidly developing subject of Multiple Dirichlet Series, an area with origins in the theory of automorphic

This book is designed both for FPGA users interested in developing new, specific components - generally for reducing execution times –and IP core designers interested in extending their catalog of spe

The topic of 'circle packing' was born of the computer age but takes its inspiration and themes from core areas of classical mathematics. A circle packing is a configuration of circles having a specified pattern of tangencies, as introduced by William Thurston in 1985. This book, first published in 2005, lays out their study, from first definitions to latest theory, computations, and applications. The topic can be enjoyed for the visual appeal of the packing images - over 200 in the book - and the elegance of circle geometry, for the clean line of theory, for the deep connections to classical topics, or for the emerging applications. Circle packing has an experimental and visual character which is unique in pure mathematics, and the book exploits that to carry the reader from the very beginnings to links with complex analysis and Riemann surfaces. There are intriguing, often very accessible, open problems throughout the book and seven Appendices on subtopics of independent interest. Th

In Contributions to Automorphic Forms, Geometry, and Number Theory, Haruzo Hida, Dinakar Ramakrishnan, and Freydoon Shahidi bring together a distinguished group of experts to explore automorphic form

This volume is an outgrowth of the LMS Durham Symposium on L-functions, held in July 1989. The symposium consisted of several short courses, aimed at presenting rigorous but non-technical expositions of the latest research areas, and a number of individual lectures on specific topics. The contributors are all outstanding figures in the area of algebraic number theory and this volume will be of lasting value to students and researchers working in the area.

The theory of arithmetical functions has always been one of the more active parts of the theory of numbers. The large number of papers in the bibliography, most of which were written in the last forty

Arithmetic Functions and Integer Products presents an algebraically oriented approach to the theory of additive and multiplicative arithmetic functions. This is a very active theory with applications

This graduate-level text offers a concise but wide-ranging introduction to methods of approximating continuous functions by functions depending only on a finite number of parameters. It places particu

The theory of automorphic forms is playing increasingly important roles in several branches of mathematics, even in physics, and is almost ubiquitous in number theory. This book introduces the reader

A full, clear introduction to the properties and applications of Bessel functions, this self-contained text is equally useful for the classroom or for independent study. Topics include Bessel fu

Explores concept of probability, surveys rules for addition and multiplication of probabilities, conditional probability, total probability, Bayes formula, Bernoulli's scheme, random variables, the C

This book includes information on elementary general topology, the Cauchy Integral Theorem and concepts of homology and homotopy in their application to the Cauchy theory. It is intended for an introd

Right triangles are at the heart of this textbook’s vibrant new approach to elementary number theory. Inspired by the familiar Pythagorean theorem, the author invites the reader to ask natural arithme

This monograph provides a brief exposition of automorphic forms of weight 1 and their applications to arithmetic, especially to Galois representations. One of the outstanding problems in arithmetic is

The subjects treated in this book have been especially chosen to represent a bridge connecting the content of a first course on the elementary theory of analytic functions with a rigorous treatment of

L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students with a basic knowledge of classical analysis, complex variable theory, and algebra. Also within the volume are many new results not yet found in the literature. The exposition provides complete detailed proofs of results in an easy-to-read format using many examples and without the need to know and remember many complex definitions. The main themes of the book are first worked out for GL(2,R) and GL(3,R), and then for the general case of GL(n,R). In an appendix to the book, a set of Mathematica functions is presented, designed to allow the reader to explore the theory from a computational point of view.

Introductory textbook in the important area of network security for undergraduate and graduate students‧ Comprehensively covers fundamental concepts with newer topics such as electronic cash, bit-coin

Brief but intriguing monograph on the theory of elliptic functions, written by a prominent mathematician. Spotlights high points of the fundamental regions and illustrates powerful, versatile analytic

In this concise yet comprehensive guide to the mathematics of modern portfolio theory the authors discuss mean-variance analysis, factor models, utility theory, stochastic dominance, very long term investing, the capital asset pricing model, risk measures including VAR, coherence, market efficiency, rationality and the modelling of actuarial liabilities. Each topic is clearly explained with assumptions, mathematics, limitations, problems and solutions presented in turn. Joshi's trademark style of clarity and practicality is here brought to classical financial mathematics. The book is suitable for mathematically trained students in actuarial studies, business and economics as well as mathematics and finance, and it can be used for both self-study and as a course text. The authors' experience as both academics and practitioners brings clarity and relevance to the book, whilst ensuring that the limitations of models are highlighted.

This book presents a comprehensive introduction to concepts of almost periodicity, asymptotic almost periodicity, almost automorphy, asymptotic almost automorphy, pseudo-almost periodicity and pseudo-

This graduate-level textbook provides an elementary exposition of the theory of automorphic representations and L-functions for the general linear group in an adelic setting. Definitions are kept to a minimum and repeated when reintroduced so that the book is accessible from any entry point, and with no prior knowledge of representation theory. The book includes concrete examples of global and local representations of GL(n), and presents their associated L-functions. In Volume 1, the theory is developed from first principles for GL(1), then carefully extended to GL(2) with complete detailed proofs of key theorems. Several proofs are presented for the first time, including Jacquet's simple and elegant proof of the tensor product theorem. In Volume 2, the higher rank situation of GL(n) is given a detailed treatment. Containing numerous exercises by Xander Faber, this book will motivate students and researchers to begin working in this fertile field of research.

This graduate-level textbook provides an elementary exposition of the theory of automorphic representations and L-functions for the general linear group in an adelic setting. Definitions are kept to a minimum and repeated when reintroduced so that the book is accessible from any entry point, and with no prior knowledge of representation theory. The book includes concrete examples of global and local representations of GL(n), and presents their associated L-functions. In Volume 1, the theory is developed from first principles for GL(1), then carefully extended to GL(2) with complete detailed proofs of key theorems. Several proofs are presented for the first time, including Jacquet's simple and elegant proof of the tensor product theorem. In Volume 2, the higher rank situation of GL(n) is given a detailed treatment. Containing numerous exercises by Xander Faber, this book will motivate students and researchers to begin working in this fertile field of research.

A comprehensive guide to the nature of language and an introduction to linguistic analysis.>

Starting from an elementary level Professor Jones discusses generalised functions and their applications. He aims to supply the simplest introduction for those who wish to learn to use generalised functions and there is liberal provision of exercises with which to gain experience. The study of more advanced topics such as partial differential equations, Laplace transforms and ultra-distributions should also make it a valuable source for researchers. The demands placed upon the reader's analytical background are the minimum required to approach this topic. Therefore, by selecting chapters it is possible to construct a short introductory course for students, a final-year option for honours undergraduates or a comprehensive postgraduate course.

L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students with a basic knowledge of classical analysis, complex variable theory, and algebra. Also within the volume are many new results not yet found in the literature. The exposition provides complete detailed proofs of results in an easy-to-read format using many examples and without the need to know and remember many complex definitions. The main themes of the book are first worked out for GL(2,R) and GL(3,R), and then for the general case of GL(n,R). In an appendix to the book, a set of Mathematica functions is presented, designed to allow the reader to explore the theory from a computational point of view.