Automorphic Forms and Geometry of Arithmetic Varieties

Released on by K. Hashimoto
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  • Automorphic Forms and Geometry of Arithmetic Varieties Book Detail

  • Author : K. Hashimoto
  • Release Date : 2014-07-14
  • Publisher : Academic Press
  • Genre : Mathematics
  • Pages : 540
  • ISBN 13 : 1483218074
  • File Size : 10,10 MB
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Automorphic Forms and Geometry of Arithmetic Varieties by K. Hashimoto PDF Summary

Book Description: 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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Automorphic Forms and Applications

Automorphic Forms and Applications

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The theory of automorphic forms has seen dramatic developments in recent years. In particular, important instances of Langlands functoriality have been establis