Introduction to Siegel Modular Forms and Dirichlet Series

Häftad, Engelska, 2008

747 kr

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Beskrivning

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).

Produktinformation

Utgivningsdatum:2008-12-22
Mått:155 x 235 x 11 mm
Vikt:306 g
Format:Häftad
Språk:Engelska
Serie:Universitext
Antal sidor:184
Upplaga:2009
Förlag:Springer-Verlag New York Inc.
ISBN:9780387787527

Utforska kategorier

Matematik inom Naturvetenskap och teknik

Recensioner i media

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)