11 By Ralf Schmidt (Univ. Saarland)

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(1)Proceedings of Japanese-German Seminar “Explicit structures of modular forms and zeta functions”. Table of Contents. 1. New Points of View on the Selberg Zeta Function . . . . . . . 1 By Don Zagier (Max Planck Institut für mathematik). 2. The Saito-Kurokawa Lifting and Langlands Functoriality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 By Ralf Schmidt (Univ. Saarland). 3. Critical Values of Triple L functions . . . . . . . . . . . . . . . . . . . . . .20 By Siegfried Böcherer (Univ. Mannheim). 4. L-functions and Equidistribution of Measures on the Sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 By Rainer Schulze-Pillot (Univ. Saarland). 5. Exact Values of the Standard Zeta Functions . . . . . . . . . . . 32 By Hidenori Katsurada (Muroran Institute Tech.).

(2) 6. Trace Identity on Twisting Operators of Half-integral Weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 By Masaru Ueda (Nara Women Univ.).

(3) 7. On a p-adic Eisenstein Series(joint work with H. Katsurada) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 By Shoyu Nagaoka (Kinki Univ.). 8. On Some Construction of Siegel Cusp Forms . . . . . . . . . . . . 58 By Tamotsu Ikeda (Kyoto Univ.). 9. Fourier Coeﬃcients of Holomorphic Eisenstein Series . . 63 By Winfried Kohnen (Univ. Heidelberg). 10. Local Picard Groups and Theta Series . . . . . . . . . . . . . . . . . . . 69 By Jan Bruinier (Univ. Heidelberg). 11. Comparison of Diﬀerent Models of the Moduli Space Marked Cubic Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 By Eberhard Freitag (Univ. Heidelberg). 12. A Lifting Conjecture on Siegel Modular Forms of Halfintegral Weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 By Shuichi Hayashida and Tomoyoshi Ibukiyama (Osaka Univ.). 13. Fourier-Jacobi Expansion of Kudla Lift . . . . . . . . . . . . . . . . . . 90 By Atsushi Murase (Kyoto Sangyo Univ.) and Takashi Sugano (Kanazawa Univ.). 14. Estimating the Dimension of the Space of Siegel Modular Forms of Genus 2 with Level 2 and 3. . . . . . . . . . . . . . . . . . . 101.

(4) By Hiroki Aoki(Ritsumeikan Univ.). 15. Motives and Siegel Modular Forms . . . . . . . . . . . . . . . . . . . . . 107 By Hiroyuki Yoshida (Kyoto Univ.). 16. Teichmüller Modular Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 By Takashi Ichikawa (Saga Univ.). 17. Some Remarks on Exceptional Groups and Domains . .121 By Ichiro Satake. 18. Modular Forms Methods for Bounding Kissing Numbers, Regulators and Covolumes of Arithmetic Groups . . . . . 132 By Nils-Peter Skoruppa (Univ. Siegen). 19. Modular Cycles on Arithmetic Quotients of Classical Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 By Takayuki Oda (Univ. Tokyo). 20. Sup-norm Bounds for Automorphic Forms in the Cocompact Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 By Jay Jorgenson (City Coll. New York) and Jürg Kramer (Humboldt Univ.). 21. Eichler Orders of High Power Levels: Type Number and Linear Relations of Theta Series . . . . . . . . . . . . . . . . . . . . . . . . . 160 By Ki-ichiro Hashimoto (Waseda Univ.).

(5) 22. The Hardy-Littlewood Property of Flag Varieties . . . . . 167 By Takao Watanabe (Osaka Univ.). 23. Local Theta Correspondences for U (n, n) and R-groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 By Atsushi Ichino (Kyoto Univ.).

(6) 24. Functional Equations of Prehomogeneous Zeta Functions and Intertwining Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 By Fumihiro Sato (Rikkyo Univ.). 25. On Real Maass Lifts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 By Rolf Berndt (Univ. Hamburg). 26. Some Graded Rings of Hermitian Modular Forms . . . . . 199 By Aloys Krieg (Univ. Aachen). 27. Mellin Transforms of Whittaker Functions . . . . . . . . . . . . . 204 By Anton Deitmar (Univ. Exeter). 28. Some Examples of Zeta Functions of Prehomogeneous Vector Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 By Hiroshi Saito (Kyoto Univ.). 29. On Siegel Eisenstein Series Attached to Certain Nontempered Zuckerman Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 By Takuya Miyazaki(Keio Univ.). 30. Twisted Endoscopy and the Generic Packet Conjecture 222 By Takuya Konno(Kyushu Univ.). 31. Spherical Functions on Some Spherical Homogeneous Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 By Yumiko Hironaka (Waseda Univ.).

(7) 32. Selberg Zeta Functions and the Shimura Correspondence for Mass Wave Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 By Tsuneo Arakawa (Rikkyo Univ.).

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