Explicit Shimura’s conjecture for Sp3 on a computer

Kirill Vankov (1) , Alexei Pantchichkine (1)

1 IF - Institut Fourier

We compute by a different method the generating series in Shimura's conjecture for Sp3, proved by Andrianov in 1967. We develop formulas for the Satake spherical maps for Spn and GLn.

Domaines: Théorie des nombres [math.NT]

Kirill Vankov, Alexei Pantchichkine. Explicit Shimura’s conjecture for Sp3 on a computer. Mathematical Research Letters, 2007, 2, pp.173-187. ⟨10.4310/MRL.2007.v14.n2.a2⟩. ⟨hal-01571077⟩