New PDF release: Automorphic Forms And Zeta Functions: Proceedings of the

By Siegfried Bocherer, Tomoyoshi Ibukiyama, Masanobu Kaneko, Fumihiro Sato

ISBN-10: 9812566325

ISBN-13: 9789812566324

ISBN-10: 9812774416

ISBN-13: 9789812774415

This quantity incorporates a invaluable choice of articles offered at a convention on Automorphic types and Zeta features in reminiscence of Tsuneo Arakawa, an eminent researcher in modular varieties in numerous variables and zeta features. The e-book starts with a assessment of his works, through sixteen articles via specialists within the fields together with H Aoki, R Berndt, okay 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 number of themes within the concept of modular kinds and zeta features are lined: Theta sequence and the root difficulties, Jacobi types, automorphic varieties on Sp(1, q), double zeta features, distinct values of zeta and L-functions, a lot of that are heavily relating to Arakawa's works. This selection of papers illustrates Arakawa's contributions and the present developments in modular types in numerous variables and similar zeta features.

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Additional resources for Automorphic Forms And Zeta Functions: Proceedings of the Conference in Memory of Tsuneo Arakawa Rikkyo University, Japan 4-7 September 2004

Sample text

S) > n -f 1 holds, therefore we have no problems of convergence). It is easily seen that for 7 ^ = ( I e r%(N)oo and 7 e Tfi(N) we have EZ&x^ov • R-l,s) = det(D)-kxh) • E%(Z,x,R,s). Therefore these Eisenstein series depend (essentially) only on the double cosets rsWoo-R-rsw, moreover this series is zero unless the important compatibilty condition xiR-'looR) = det(D)~k is satified for all 7 ^ e (RT^(N)R-1) n r#(iV)oo. We can parametrize the double cosets of i2 = I J by the p^-rank of C (1 < i

J. , 16-3, 2005, 249279. 2. E. Freitag, Hilbert modular forms, Springer, 1990. 3. K. B. Gundlach, Die Bestimmung der Funktionen zur Hilbertschen Modulgruppe des Zahlkorpers Q(\/5), Math. , 152, 1963, 226-256. 4. K. B. Gundlach, Die Bestimmung der Funktionen zu einigen Hilbertschen Modulgruppen, J. Reine Angew. , 220, 1965, 109-153. 5. Y. Hamahata, Hilbert Hokeikeishikikan (Japanese), The First Spring Conference of Modular Forms and Related Topics, 2002, 43-77. 6. T. Ibukiyama, On differential operators on automorphic forms and invariant pluri-harmonic polynomials, Comment.

In this section, we prove the analogous result on Hilbert modular forms. Dimensions of Hilbert Modular Forms 27 For Fi 6 Akl, F2 £ Aki and F3 € Ak3, put / hF! k2F2 k3F3 \ £ * /-«^ F ' [FuF2,F3]:=det OTi OTi C/Ti A F l A F2 A Fa \6V 2 [Fi,F By direct calculation, we have [G2,G3,GA]eA^+. <9T2 6 2,F3] 0T2 fc )fc 2. 1. There exists a non-zero constant c such that [G2, G3, G4] = cG$Gs Proof. Because dimAj^" = 1, there exists c £ C such that [G2,G3,Gi] cG

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Automorphic Forms And Zeta Functions: Proceedings of the Conference in Memory of Tsuneo Arakawa Rikkyo University, Japan 4-7 September 2004 by Siegfried Bocherer, Tomoyoshi Ibukiyama, Masanobu Kaneko, Fumihiro Sato


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