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Full Description
This volume contains a valuable collection of articles presented at a conference on Automorphic Forms and Zeta Functions in memory of Tsuneo Arakawa, an eminent researcher in modular forms in several variables and zeta functions. The book begins with a review of his works, followed by 16 articles by experts in the fields including H Aoki, R Berndt, K Hashimoto, S Hayashida, Y Hironaka, H Katsurada, W Kohnen, A Krieg, A Murase, H Narita, T Oda, B Roberts, R Schmidt, R Schulze-Pillot, N Skoruppa, T Sugano, and D Zagier. A variety of topics in the theory of modular forms and zeta functions are covered: Theta series and the basis problems, Jacobi forms, automorphic forms on Sp(1, q), double zeta functions, special values of zeta and L-functions, many of which are closely related to Arakawa's works.This collection of papers illustrates Arakawa's contributions and the current trends in modular forms in several variables and related zeta functions.
Contents
# Tsuneo Arakawa and His Works # Estimate of the Dimensions of Hilbert Modular Forms by Means of Differential Operators (H Aoki) # Marsden-Weinstein Reduction, Orbits and Representations of the Jacobi Group (R Berndt) # On Eisenstein Series of Degree Two for Squarefree Levels and the Genus Version of the Basis Problem I (S Bocherer) # Double Zeta Values and Modular Forms (H Gangl et al.) # Type Numbers and Linear Relations of Theta Series for Some General Orders of Quaternion Algebras (K-I Hashimoto) # Skew-Holomorphic Jacobi Forms of Higher Degree (S Hayashida) # A Hermitian Analog of the Schottky Form (M Hentschel & A Krieg) # The Siegel Series and Spherical Functions on O(2n)/(O(n) x O(n)) (Y Hironaka & F Sato) # Koecher-Maas Series for Real Analytic Siegel Eisenstein Series (T Ibukiyama & H Katsurada) # A Short History on Investigation of the Special Values of Zeta and L-Functions of Totally Real Number Fields (T Ishii & T Oda) # Genus Theta Series, Hecke Operators and the Basis Problem for Eisenstein Series (H Katsurada & R Schulze-Pillot) # The Quadratic Mean of Automorphic L-Functions (W Kohnen et al.) # Inner Product Formula for Kudla Lift (A Murase & T Sugano) # On Certain Automorphic Forms of Sp(1,q) (Arakawa's Results and Recent Progress) (H-A Narita) # On Modular Forms for the Paramodular Groups (B Roberts & R Schmidt) # SL(2,Z)-Invariant Spaces Spanned by Modular Units (N-P Skoruppa & W Eholzer)
