Introduction to Siegel Modular Forms and Dirichlet Series by Anatoli Andrianov

Introduction to Siegel Modular Forms and Dirichlet Series

byAnatoli Andrianov

Paperback | December 22, 2008

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This is intended for a graduate course on Siegel modular forms, Hecke operators, and related zeta functions. The author's aim is to present a concise and self-contained introduction to an important and developing area of number theory that will serve to attract young researchers to this beautiful field.Topics include:* analytical properties of radial Dirichlet series attached to modular forms of genuses 1 and 2;* the abstract theory of Hecke-Shimura rings for symplectic and related groups;* action of Hecke operators on Siegel modular forms;* applications of Hecke operators to a study of multiplicative properties of Fourier coefficients of modular forms;* Hecke zeta functions of modular forms in one variable and to spinor (or Andrianov) zeta functions of Siegel modular forms of genus two;* the proof of analytical continuation and functional equation (under certain assumptions) for Euler products associated with modular forms of genus two.This text contains a number of exercises and the only prerequisites are standard courses in Algebra and Calculus (one and several variables).

Details & Specs

Title:Introduction to Siegel Modular Forms and Dirichlet SeriesFormat:PaperbackDimensions:196 pages, 9.25 × 6.1 × 0 inPublished:December 22, 2008Publisher:Springer New YorkLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0387787526

ISBN - 13:9780387787527

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Table of Contents

Preface.- Introduction: The Two Features of Arithmetical Zeta Functions.- Modular Forms.- Dirichlet Series of Modular Forms.- Hecke-Shimura Rings of Double Cosets.- Hecke Operators.- Euler Factorization of Radial Series.- Conclusion: Other Groups, Other Horizons.- Notes.- Short Bibliography.-

Editorial Reviews

From the reviews:"Introduction to Siegel Modular Forms and Dirichlet Series is a compact but masterful presentation of this important generalization of the classical theory, and a good deal more. . beneficiaries of this wonderful book are the obvious candidates: students of number theory with their qualifying examinations behind them, or very gifted undergraduates who have already learned group theory and complex analysis, some topology, some rings and fields, and so on." (Michael Berg, The Mathematical Association of America, May, 2009)"Andrianov . offers a comparatively concrete, lowbrow treatment of Siegel modular forms, a large and important but still special class of higher-dimensional modular forms. Readers familiar with standard accounts of the one-dimensional story will find the flow and organization here comfortingly familiar . . Andrianov has suppressed entirely the vantage of algebraic geometry, presumably for simplicity. . Summing Up: Highly recommended. Upper-division undergraduate through professional collections." (D. V. Feldman, Choice, Vol. 47 (4), December, 2009)"The book under review is a concise and self-contained introduction to the Hecke theory of Siegel modular forms and zeta functions and is suitable for beginners. . Siegel modular form is introduced and its analytic properties are investigated." (Hidenori Katsurada, Mathematical Reviews, Issue 2010 f)