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

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

ISBN-10: 9812566325

ISBN-13: 9789812566324

"This quantity incorporates a number of articles provided at a convention on Automorphic types and Zeta capabilities in reminiscence of Tsuneo Arakawa, an eminent researcher in modular kinds in numerous variables and zeta capabilities. The publication starts off with a assessment of his works, through sixteen articles through specialists within the fields. This selection of papers illustrates Arakawa's contributions and the present developments in modular kinds in numerous variables and comparable zeta services.

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Additional resources for Automorphic Forms and Zeta Functions: Proceedings of the Conference in Memory of Tsuneo Arakawa Rikkyo University

Sample text

5 Gundlach [3] determined the generators and the dimension of Hilbert modular forms on Q(%/5). There exist four generators Z2,Z^,Z& and Z15 of weight 2 , 5 , 6 and 15. T h e dimension of weight k is the coefficient of xk on the formal power series development of 1 + z15 (l-a;2)(l-a;5)(l-a;6)' There exists a non-zero constant z such t h a t [Z2,Z5,ZQ] — ZZ15. References 1. H. Aoki and T. Ibukiyama, Simple Graded Rings of Siegel Modular Forms, Differential Operators and Borcherds Products, Int. J.

And we have a moment map * : M x Q~ —• 6*, (m, rj) H-> $(m) - 77 Representations of the Jacobi Group 31 where $ is the if-moment map coming from the injection L : M <^-> g* composed with the restriction from g* to 6*. Then one has the MarsdenWeinstein reduction Mo:=Mteti y-1{0)/K = which will be identfied with $_1(r/)/i;£rT;, K„ the stabilizing group of 77 G t*. ). This way, at least in some special cases one has precise information: \ does not appear in it if Mo is empty. And the multiplicity is one if Mo is just a point.

P \ 7). Here c has to be coprime to p (because of the F p -rank of C) and c / ^ u i o ^ N mod \M3CW! U3CLJ3J and from this p I ui = n. + £r2 The only possibility here is P\n, t = o. Then the conditions (*) are satisfied for (C, D) at least locally at p. Therefore the conditions are in this case P\c, U= ( 1 0 ) mod p 54 S. Bocherer The subcase p \ Ni, I coprime to p. This is the most complicated case. We may assume that p | a. We also have the condition p \ CLJX . * We assume that p \ r\: Then t 1 10 U = mod p and C= (° ( - ^ 2 + ^ ) 7 0 —du)2j mod p.

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Automorphic Forms and Zeta Functions: Proceedings of the Conference in Memory of Tsuneo Arakawa Rikkyo University by Siegfried Bocherer, Tomoyoshi Ibukiyama, Masanobu Kaneko, Fumihiro Sato


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