Zeta Functions

September 18 - 22, 2006, Moscow, Russia

Laboratoire J.-V. Poncelet

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Alexey Panchishkin

Institut Fourier, France

Explicit form of Shimura's conjecture for S_p3

We find an explicit solution in Shimura's conjecture for Sp3 (1963). The existence of the solution was established for any genus n by A.N.Andrianov. We develop formulas for the Satake spherical maps for Sp_n and Gl_n.