Abstract
We investigate the asymptotic distribution of integrals of the -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 that is uniform in every parameter. To establish this estimate we prove a variant of Kuznetsov’s formula where the spectral data is restricted to half-integral weight forms in the Kohnen plus space, and we apply Young’s hybrid subconvexity estimates for twisted modular -functions.
Citation
Nickolas Andersen. William D. Duke. "Modular invariants for real quadratic fields and Kloosterman sums." Algebra Number Theory 14 (6) 1537 - 1575, 2020. https://doi.org/10.2140/ant.2020.14.1537
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