Download Automorphic Forms And Zeta Functions: Proceedings of the by Siegfried Bocherer, Tomoyoshi Ibukiyama, Masanobu Kaneko, PDF

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

ISBN-10: 9812566325

ISBN-13: 9789812566324

ISBN-10: 9812774416

ISBN-13: 9789812774415

This quantity encompasses a important selection of articles offered at a convention on Automorphic varieties and Zeta capabilities in reminiscence of Tsuneo Arakawa, an eminent researcher in modular varieties in numerous variables and zeta services. The e-book starts off with a evaluation of his works, via sixteen articles by way of specialists within the fields together with H Aoki, R Berndt, ok 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. numerous issues within the concept of modular kinds and zeta services are lined: Theta sequence and the root difficulties, Jacobi kinds, automorphic kinds on Sp(1, q), double zeta features, unique values of zeta and L-functions, a lot of that are heavily with regards to Arakawa's works. This selection of papers illustrates Arakawa's contributions and the present developments in modular types in different variables and comparable zeta capabilities.

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

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On poly-Bernoulli numbers. Comment. Math. Univ. St. Paul. 48 (1999), no. 2, 159-167. (with M. Kaneko) 24. A note on the restriction map for Jacobi forms. Abh. Math. Sem. Univ. Hamburg 69 (1999), 309-317. (with S. Bocherer) 25. Saito-Kurokawa lifting for odd weights. Comment. Math. Univ. St. Paul. 49 (2000), no. 2, 159-176. 26. Converse theorem for not necessarily cuspidal Siegel modular forms of degree 2 and Saito-Kurokawa lifting. Comment. Math. Univ. St. Paul. 50 (2001), no. 2, 197-234. (with I.

If v < —r, then c(r, u) = c(r, —v) = 0. ,r) Dimensions of Hilbert Modular Forms 25 and c(r,v) = c(r, —v). Then we have (I 1 . . 1 \ / c ( r , 0 ) \ 0 l2 ... r 2c(r, 1) \0 l2r 2r / /°\ W \2c(r,r)/ By the Vandermonde formula, we have c(r, v) = 0. D 2n (J4fc+(2ri)) C M2k+4n{n)- The similar lemma holds for A~£~, A^+ or A^~• Consequently, we have the following proposition. 2. For any non-negative integer n, there exist four exact sequences 0 0 0 0 • A£+(2n+2) A+ + (2n) D2„ A*2fc+4n(n), I>2T. • A+-(2n + 2) A+"(2n) - ^ = - > M 2fc+4 „(n + l), + > j4* (2n + 3) V ( 2 n + 1) _ > AjT (2n + 3) £>2n + l M 2 f c + 4 „ + 2 (n + 2), M 2 fc + 4 n + 2 (n + l ) .

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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