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# ๐ Arithmeticity in the theory of automorphic forms by Goro Shimura โ download pdf

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The main objects of study in this book are Eisenstein series and zeta functions associated with Hecke eigenforms on symplectic and unitary groups. After preliminaries--including a section, "Notation and Terminology"--the first part of the book deals with automorphic forms on such groups. In particular, their rationality over a number field is defined and discussed in connection with the group action; also the reciprocity law for the values of automorphic functions at CM-points is proved. Next, certain differential operators that raise the weight are investigated in higher dimension. The notion of nearly holomorphic functions is introduced, and their arithmeticity is defined. As applications of these, the arithmeticity of the critical values of zeta functions and Eisenstein series is proved. Though the arithmeticity is given as the ultimate main result, the book discusses many basic problems that arise in number-theoretical investigations of automorphic forms but that cannot be found in expository forms. Examples of this include the space of automorphic forms spanned by cusp forms and certain Eisenstein series, transformation formulas of theta series, estimate of the Fourier coefficients of modular forms, and modular forms of half-integral weight. All these are treated in higher-dimensional cases. The volume concludes with an Appendix and an Index. The book will be of interest to graduate students and researchers in the field of zeta functions and modular forms

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- Series:
**Mathematical Surveys and Monographs 082** - Author:
**Goro Shimura** - Year:
**2000** - Publisher:
**American Mathemataical Society** - Language:
**English** - ISBN:
**0821849611,978-0-8218-4961-3,0-8218-2671-9,31-1979-561-5,121-1995-21-6**

- DPI:
**600** - File size:
**3 981 594** - Format:
**djvu**

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The book is based on the notes from the graduate course given by the author at Rutgers University in the fall of 1994 and the spring of 1995. The main goal of the book is to acquaint the reader with various perspectives of the theory of automorphic forms....

This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincarรฉ upper half plane.ย This book is intended for beginning graduate students in mathematics or researchers in physi...

The central theme of this book is an invariant attached to an ideal class of a totally real algebraic number field. This invariant provides us with a unified understanding of periods of abelian varieties with complex multiplication and the Stark-Shintani ...

The latest developments on both the theory and applications of bifurcations with symmetry. The text includes recent experimental work as well as new approaches to and applications of the theory to other sciences. It shows the range of dissemination of the...

This book develops a new cohomological theory for schemes in positive characteristic $p$ and it applies this theory to give a purely algebraic proof of a conjecture of Goss on the rationality of certain $L$-functions arising in the arithmetic of function ...

The basic theory of sheet metal forming in the automotive, appliance and aircraft industries is given. This fills a gap between the descriptive treatments in most manufacturing texts and the advanced numerical methods used in computer-aided-design systems...

This introductory textbook is designed to teach undergraduates the basic ideas and techniques of number theory, with special consideration to the principles of analytic number theory. The first five chapters treat elementary concepts such as divisibility,...

Presents new research revealing the interplay between classical analysis and modern computation and complexity theory. Two intimately interwoven threads run though the text: the arithmetic-geometric mean (AGM) iteration of Gauss, Lagrange, and Legendre an...

Much progress has been made in many areas of concrete technology since the publication of the first edition of Concrete. For those familiar with the first edition, very little has been removed, while the chapters on cements, aggregates, chemical admixture...

Land remote sensing: the use of space-based satellite technologies to obtain information on environmental variables such as land-use and land-covering combination with other types of data can provide information on changes in the Earth's surface and atmos...

The corrosion of reinforcing steel in concrete is a major problem facing civil engineers and surveyors throughout the world today....

Written by an array of international experts, this book provides a comprehensive a comprehensive analysis of the key scientific and technological advances that ensure the quality of cotton is maintained from the field to the fabric. It begins with a discu...

Chemical Engineering Volume 2 covers the properties of particulate systems, including the character of individual particles and their behaviour in fluids. Sedimentation of particles, both singly and at high concentrations, flow in packed and fluidised be...

The development of cryogenic devices for particle detection has reached a stage at which many interesting applications are conceivable and already have been demonstrated. The book provides a comprehensive review of the field of cryogenic particle detectio...