edited by Siegfried Böcherer (Universität Mannheim, Germany) , Tomoyoshi Ibukiyama (Osaka University, Japan) , Masanobu Kaneko (Kyushu University, Japan) , & Fumihiro Sato (Rikkyo University, Japan)

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.

• 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 Böcherer)
• 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–Maaß 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)