Arithmetic And Analytic Theories Of Quadratic Forms And Clifford Groups

Author : Goro Shimura
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 50,7 Mb
Release : 2014-05-27
Category : Education
ISBN : 9781470415624

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Arithmetic and Analytic Theories of Quadratic Forms and Clifford Groups by Goro Shimura Pdf

In this book, award-winning author Goro Shimura treats new areas and presents relevant expository material in a clear and readable style. Topics include Witt's theorem and the Hasse principle on quadratic forms, algebraic theory of Clifford algebras, spin groups, and spin representations. He also includes some basic results not readily found elsewhere. The two principle themes are: (1) Quadratic Diophantine equations; (2) Euler products and Eisenstein series on orthogonal groups and Clifford groups. The starting point of the first theme is the result of Gauss that the number of primitive representations of an integer as the sum of three squares is essentially the class number of primitive binary quadratic forms. Presented are a generalization of this fact for arbitrary quadratic forms over algebraic number fields and various applications. For the second theme, the author proves the existence of the meromorphic continuation of a Euler product associated with a Hecke eigenform on a Clifford or an orthogonal group. The same is done for an Eisenstein series on such a group. Beyond familiarity with algebraic number theory, the book is mostly self-contained. Several standard facts are stated with references for detailed proofs. Goro Shimura won the 1996 Steele Prize for Lifetime Achievement for "his important and extensive work on arithmetical geometry and automorphic forms".

Author : Wai Kiu Chan,Lenny Fukshansky,Rainer Schulze-Pillot,Jeffrey D. Vaaler
Publisher : American Mathematical Soc.
Page : 259 pages
File Size : 49,6 Mb
Release : 2013
Category : Mathematics
ISBN : 9780821883181

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Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms by Wai Kiu Chan,Lenny Fukshansky,Rainer Schulze-Pillot,Jeffrey D. Vaaler Pdf

This volume contains the proceedings of the International Workshop on Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms. The articles cover the arithmetic theory of quadratic forms and lattices, as well as the effective Diophantine analysis with height functions.

Author : Burton W Jones
Publisher : American Mathematical Soc.
Page : 212 pages
File Size : 41,9 Mb
Release : 1950-12-31
Category : Forms, Binary
ISBN : 9781614440109

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The Arithmetic Theory of Quadratic Forms by Burton W Jones Pdf

This monograph presents the central ideas of the arithmetic theory of quadratic forms in self-contained form, assuming only knowledge of the fundamentals of matric theory and the theory of numbers. Pertinent concepts of p -adic numbers and quadratic ideals are introduced. It would have been possible to avoid these concepts, but the theory gains elegance as well as breadth by the introduction of such relationships. Some results, and many of the methods, are here presented for the first time. The development begins with the classical theory in the field of reals from the point of view of representation theory; for in these terms, many of the later objectives and methods may be revealed. The successive chapters gradually narrow the fields and rings until one has the tools at hand to deal with the classical problems in the ring of rational integers. The analytic theory of quadratic forms is not dealt with because of the delicate analysis involved. However, some of the more important results are stated and references are given.

Author : Ricardo Baeza
Publisher : American Mathematical Soc.
Page : 424 pages
File Size : 53,5 Mb
Release : 2009-08-14
Category : Mathematics
ISBN : 9780821846483

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Quadratic Forms -- Algebra, Arithmetic, and Geometry by Ricardo Baeza Pdf

This volume presents a collection of articles that are based on talks delivered at the International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms held in Frutillar, Chile in December 2007. The theory of quadratic forms is closely connected with a broad spectrum of areas in algebra and number theory. The articles in this volume deal mainly with questions from the algebraic, geometric, arithmetic, and analytic theory of quadratic forms, and related questions in algebraic group theory and algebraic geometry.

Author : Goro Shimura
Publisher : Springer Science & Business Media
Page : 245 pages
File Size : 46,5 Mb
Release : 2010-08-09
Category : Mathematics
ISBN : 9781441917324

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Arithmetic of Quadratic Forms by Goro Shimura Pdf

This book is divided into two parts. The first part is preliminary and consists of algebraic number theory and the theory of semisimple algebras. There are two principal topics: classification of quadratic forms and quadratic Diophantine equations. The second topic is a new framework which contains the investigation of Gauss on the sums of three squares as a special case. To make the book concise, the author proves some basic theorems in number theory only in some special cases. However, the book is self-contained when the base field is the rational number field, and the main theorems are stated with an arbitrary number field as the base field. So the reader familiar with class field theory will be able to learn the arithmetic theory of quadratic forms with no further references.

Author : Krishnaswami Alladi,Manjul Bhargava,David Savitt,Pham Huu Tiep
Publisher : Springer Science & Business Media
Page : 303 pages
File Size : 46,5 Mb
Release : 2013-08-13
Category : Mathematics
ISBN : 9781461474883

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Quadratic and Higher Degree Forms by Krishnaswami Alladi,Manjul Bhargava,David Savitt,Pham Huu Tiep Pdf

In the last decade, the areas of quadratic and higher degree forms have witnessed dramatic advances. This volume is an outgrowth of three seminal conferences on these topics held in 2009, two at the University of Florida and one at the Arizona Winter School. The volume also includes papers from the two focused weeks on quadratic forms and integral lattices at the University of Florida in 2010.Topics discussed include the links between quadratic forms and automorphic forms, representation of integers and forms by quadratic forms, connections between quadratic forms and lattices, and algorithms for quaternion algebras and quadratic forms. The book will be of interest to graduate students and mathematicians wishing to study quadratic and higher degree forms, as well as to established researchers in these areas. Quadratic and Higher Degree Forms contains research and semi-expository papers that stem from the presentations at conferences at the University of Florida as well as survey lectures on quadratic forms based on the instructional workshop for graduate students held at the Arizona Winter School. The survey papers in the volume provide an excellent introduction to various aspects of the theory of quadratic forms starting from the basic concepts and provide a glimpse of some of the exciting questions currently being investigated. The research and expository papers present the latest advances on quadratic and higher degree forms and their connections with various branches of mathematics.

Author : Onorato Timothy O’Meara
Publisher : Springer
Page : 354 pages
File Size : 48,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783662419229

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Introduction to Quadratic Forms by Onorato Timothy O’Meara Pdf

Author : Alexandru Buium
Publisher : American Mathematical Soc.
Page : 346 pages
File Size : 41,7 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821838624

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Arithmetic Differential Equations by Alexandru Buium Pdf

For most of the book the only prerequisites are the basic facts of algebraic geometry and number theory."--BOOK JACKET.

Author : Yu. I. Manin,Alexei A. Panchishkin
Publisher : Springer Science & Business Media
Page : 519 pages
File Size : 55,8 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9783540276920

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Introduction to Modern Number Theory by Yu. I. Manin,Alexei A. Panchishkin Pdf

This edition has been called ‘startlingly up-to-date’, and in this corrected second printing you can be sure that it’s even more contemporaneous. It surveys from a unified point of view both the modern state and the trends of continuing development in various branches of number theory. Illuminated by elementary problems, the central ideas of modern theories are laid bare. Some topics covered include non-Abelian generalizations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories.

Author : Robert Ray Bruner,John Patrick Campbell Greenlees
Publisher : American Mathematical Soc.
Page : 328 pages
File Size : 44,6 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821851890

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Connective Real $K$-Theory of Finite Groups by Robert Ray Bruner,John Patrick Campbell Greenlees Pdf

Focusing on the study of real connective $K$-theory including $ko^*(BG)$ as a ring and $ko_*(BG)$ as a module over it, the authors define equivariant versions of connective $KO$-theory and connective $K$-theory with reality, in the sense of Atiyah, which give well-behaved, Noetherian, uncompleted versions of the theory.

Author : Goro Shimura
Publisher : Springer Science & Business Media
Page : 183 pages
File Size : 51,8 Mb
Release : 2011-11-18
Category : Mathematics
ISBN : 9781461421252

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Modular Forms: Basics and Beyond by Goro Shimura Pdf

This is an advanced book on modular forms. While there are many books published about modular forms, they are written at an elementary level, and not so interesting from the viewpoint of a reader who already knows the basics. This book offers something new, which may satisfy the desire of such a reader. However, we state every definition and every essential fact concerning classical modular forms of one variable. One of the principal new features of this book is the theory of modular forms of half-integral weight, another being the discussion of theta functions and Eisenstein series of holomorphic and nonholomorphic types. Thus the book is presented so that the reader can learn such theories systematically.

Author : Joseph Albert Wolf
Publisher : American Mathematical Soc.
Page : 408 pages
File Size : 43,5 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821842898

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Harmonic Analysis on Commutative Spaces by Joseph Albert Wolf Pdf

This study starts with the basic theory of topological groups, harmonic analysis, and unitary representations. It then concentrates on geometric structure, harmonic analysis, and unitary representation theory in commutative spaces.

Author : Yiannis N. Moschovakis
Publisher : American Mathematical Soc.
Page : 521 pages
File Size : 46,7 Mb
Release : 2009-06-30
Category : Mathematics
ISBN : 9780821848135

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Descriptive Set Theory by Yiannis N. Moschovakis Pdf

Descriptive Set Theory is the study of sets in separable, complete metric spaces that can be defined (or constructed), and so can be expected to have special properties not enjoyed by arbitrary pointsets. This subject was started by the French analysts at the turn of the 20th century, most prominently Lebesgue, and, initially, was concerned primarily with establishing regularity properties of Borel and Lebesgue measurable functions, and analytic, coanalytic, and projective sets. Its rapid development came to a halt in the late 1930s, primarily because it bumped against problems which were independent of classical axiomatic set theory. The field became very active again in the 1960s, with the introduction of strong set-theoretic hypotheses and methods from logic (especially recursion theory), which revolutionized it. This monograph develops Descriptive Set Theory systematically, from its classical roots to the modern ``effective'' theory and the consequences of strong (especially determinacy) hypotheses. The book emphasizes the foundations of the subject, and it sets the stage for the dramatic results (established since the 1980s) relating large cardinals and determinacy or allowing applications of Descriptive Set Theory to classical mathematics. The book includes all the necessary background from (advanced) set theory, logic and recursion theory.

Author : A. S. Kechris
Publisher : American Mathematical Soc.
Page : 258 pages
File Size : 47,8 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821848944

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Global Aspects of Ergodic Group Actions by A. S. Kechris Pdf

A study of ergodic, measure preserving actions of countable discrete groups on standard probability spaces. It explores a direction that emphasizes a global point of view, concentrating on the structure of the space of measure preserving actions of a given group and its associated cocycle spaces.

Author : Ernst Binz,Sonja Pods
Publisher : American Mathematical Soc.
Page : 321 pages
File Size : 41,9 Mb
Release : 2008
Category : Mathematics
ISBN : 9780821844953

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The Geometry of Heisenberg Groups by Ernst Binz,Sonja Pods Pdf

"The three-dimensional Heisenberg group, being a quite simple non-commutative Lie group, appears prominently in various applications of mathematics. The goal of this book is to present basic geometric and algebraic properties of the Heisenberg group and its relation to other important mathematical structures (the skew field of quaternions, symplectic structures, and representations) and to describe some of its applications. In particular, the authors address such subjects as signal analysis and processing, geometric optics, and quantization. In each case, the authors present necessary details of the applied topic being considered." "This book manages to encompass a large variety of topics being easily accessible in its fundamentals. It can be useful to students and researchers working in mathematics and in applied mathematics."--BOOK JACKET.