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

"This quantity encompasses a number of articles offered at a convention on Automorphic types and Zeta services in reminiscence of Tsuneo Arakawa, an eminent researcher in modular types in different variables and zeta capabilities. The publication starts off with a assessment of his works, via sixteen articles via specialists within the fields. This number of papers illustrates Arakawa's contributions and the present developments in modular varieties in different variables and similar zeta features.

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

**Example text**

We have w 2 oi/) = (1/m2) dp A dq = (i/(2m2))dz Adz = (l/m2)rdr Ad

:= au>i o rp + j3u>2 ° ip evaluated at U* <* (XM, YM) (U*) = 2a ((a; + y)x'- (x1 + y') x) + (3 (pq' - p'q) . 5. The KKS-form for M£m = GJ • (k(Y* - Z*) + mR*) given in the parameters x*,y* = y* + z*,p*,q* by the symplectic form u>otp — -(2/(-2mz* +pl + q2)) (mdx* Ady* + p*dx* A dp* - q* dx* A dq* + q*dy* A dp* + p* dy*dq* +2z* dp* A dq*) . is Representations of the Jacobi Group 41 Here £« is a function of the parameters x+,y*,p*,q* fixed by the equation f(x,y*,z*,p*,q*) = 0.

St. Pauli, 48, 1999, 103118. 7. R. Miiller, Hilbertsche Modulformen und Modulfunktionen zu Q(-\/2), Math. , 266, 1983, 83-103. M A R S D E N - W E I N S T E I N R E D U C T I O N , ORBITS A N D R E P R E S E N T A T I O N S OF T H E JACOBI G R O U P ROLF BERNDT Mathematisches Seminar der Universitat Hamburg Bundesstr. de Dedicated to the memory of Tsuneo Arakawa Guillemin and Sternberg started a method to give a geometric meaning to multiplicities of representations via the Marsden-Weinstein reduction of appropriate coadjoint orbits carrying the representations.

N=0 n=0 26 H. Aoki This is the coefficient of xk on the formal power series development of ^ (1 - x2)(l - x3) (1 - x 2 )(l - x3)(l - x4)' We can prove the other three cases in an analogous way. 1 equals to the true dimension of A~£+. 1 equal to the true dimensions of A%+, A%~, A^+ and -A^" ~. Hence, if we assume the existence of these forms, we have given a new method of the determination of the dimension of Hilbert modular forms on Q(\/3)- In fact, Gundlach [4] constructed these forms G2, G3, G4, G5 and G6.