Automorphic Forms and Geometry of Arithmetic Varieties - 1st Edition - ISBN: 9780123305800, 9781483218076

Automorphic Forms and Geometry of Arithmetic Varieties

1st Edition

Editors: K. Hashimoto Y. Namikawa
eBook ISBN: 9781483218076
Imprint: Academic Press
Published Date: 28th October 1989
Page Count: 570
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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


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.


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© Academic Press 1989
Academic Press
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About the Editors

K. Hashimoto Editor

Y. Namikawa Editor