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 precious selection of articles provided 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 services. The ebook starts off with a evaluation of his works, by means of 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. quite a few issues within the concept of modular varieties and zeta features are coated: Theta sequence and the foundation difficulties, Jacobi types, automorphic kinds on Sp(1, q), double zeta capabilities, certain values of zeta and L-functions, lots of that are heavily regarding Arakawa's works. This selection of papers illustrates Arakawa's contributions and the present traits in modular kinds in different variables and comparable zeta capabilities.

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

Example text

Univ. 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.

1 . We have mult(xfc', 7T+) = 1 for k' = k + 2£,e£~N0 = 0 else. e2No by Z0(vj Wf) = 2-Km(vj ® iu<), Zi(u,- ® u/*) = (A; + j + ^)(UJ uv), F_(i>o <8> w0) = X-(v0 ® w0) = 0, Y+(VJ tt/f) = v,-+1 tt/f, -X + (u,' ® u^) = -(l/(27rm))(uj + 2 ® u>*) + (uj <8> ^ + 2 ) . e. ii{t) = 1 for £ = 0 and 1, fi(t) = 2 for t = 2 and 3, etc. 2. fc', 7r+fc) = fi(k' - k) for fc' > A;. There are several ways to realize these discrete series representations. 48ff. As elaborated in [3] and [4], these representations are also associated to coadjoint orbits of G\ resp.

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.

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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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