Automorphic Forms and Geometry of Arithmetic Varieties

Automorphic Forms and Geometry of Arithmetic Varieties

1st Edition - October 28, 1989

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  • Editors: K. Hashimoto, Y. Namikawa
  • eBook ISBN: 9781483218076

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Automorphic Forms and Geometry of Arithmetic Varieties deals with the dimension formulas of various automorphic forms and the geometry of arithmetic varieties. The relation between two fundamental methods of obtaining dimension formulas (for cusp forms), the Selberg trace formula and the index theorem (Riemann-Roch's theorem and the Lefschetz fixed point formula), is examined. Comprised of 18 sections, this volume begins by discussing zeta functions associated with cones and their special values, followed by an analysis of cusps on Hilbert modular varieties and values of L-functions. The reader is then introduced to the dimension formula of Siegel modular forms; the graded rings of modular forms in several variables; and Selberg-Ihara's zeta function for p-adic discrete groups. Subsequent chapters focus on zeta functions of finite graphs and representations of p-adic groups; invariants and Hodge cycles; T-complexes and Ogata's zeta zero values; and the structure of the icosahedral modular group. This book will be a useful resource for mathematicians and students of mathematics.

Table of Contents

  • Part I

    Zeta Functions Associated to Cones and their Special Values

    Cusps on Hilbert Modular Varieties and Values of L-Functions

    On Dimension Formula of Siegel Modular Forms

    On the Graded Rings of Modular Forms in Several Variables

    Vector Valued Modular Forms of Degree Two and their Application to Triple L-Functions

    Part II

    Special Values of L-Functions Associated with the Space of Quadratic Forms and the Representation of Sp(2n, Fp) in the Space of Siegel Cusp Forms

    Selberg-Ihara's Zeta Function for p-Adic Discrete Groups

    Zeta Functions of Finite Graphs and Representations of p-Adic Groups

    Any Irreducible Smooth GL2-Module is Multiplicity Free for any Anisotropic Torus

    A Formula for the Dimension of Spaces of Cusp Forms of Weight 1

    On Automorphism Groups of Positive Definite Binary Quaternion Hermitian Lattices and New Mass Formula

    T-Complexes and Ogata's Zeta Zero Values

    The Structure of the Icosahedral Modular Group

    Invariants and Hodge Cycles

    A Note on Zeta Functions Associated with Certain Prehomogeneous Affine Spaces

    On Zeta Functions Associated with the Exceptional Lie Groups of Type E6

    On Functional Equations of Zeta Distributions

    Multi-Tensors of Differential Forms on the Hilbert Modular Variety and on its Subvarieties, II

Product details

  • No. of pages: 570
  • Language: English
  • Copyright: © Academic Press 1989
  • Published: October 28, 1989
  • Imprint: Academic Press
  • eBook ISBN: 9781483218076

About the Editors

K. Hashimoto

Y. Namikawa

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