Sums of Kloosterman sums for real quadratic number fields

Modular Invariants for Real Quadratic Fields and Kloosterman Sums

We investigate the asymptotic distribution of integrals of the j-function that are associated to ideal classes in a real quadratic field. To estimate the error term in our asymptotic formula, we prove a bound for sums of Kloosterman sums of half-integral weight which is uniform in every parameter. To establish this estimate we prove a variant of Kuznetsov’s formula where the spectral data is re...

Real Quadratic Double Sums

In 1988, Andrews, Dyson and Hickerson initiated the study of q-hypergeometric series whose coefficients are dictated by the arithmetic in real quadratic fields. In this paper, we provide a dozen q-hypergeometric double sums which are generating functions for the number of ideals of a given norm in rings of integers of real quadratic fields and prove some related identities.

Legendre Sums, Soto-andrade Sums and Kloosterman Sums

The three sums named in the title are all known to appear in connection with the complex representation theory of GL(2, q). The first two are incarnations of certain spherical vectors, whereas the third is a matrix coefficient for a parabolic basis. In this work, Legendre and Soto-Andrade sums are shown to occur in a second way, as parabolic ClebschGordan coefficients for the tensor product of ...

Kloosterman sums for prime powers in P-adic fields

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On zeros of Kloosterman sums