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arXiv · 1608.01727

Asymptotic bounds for special values of shifted convolution Dirichlet series

Olivia Beckwith
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Abstract

Hoffstein and Hulse defined the shifted convolution series of two cusp forms by "shifting" the usual Rankin-Selberg convolution L-series by a parameter h. We use the theory of harmonic Maass forms to study the behavior in h-aspect of certain values of these series and prove a polynomial bound as h approaches infinity. Our method relies on a result of Mertens and Ono, who showed that these values are Fourier coefficients of mixed mock modular forms.

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Olivia Beckwith. 2016-08-05. Asymptotic bounds for special values of shifted convolution Dirichlet series. https://arxiv.org/abs/1608.01727

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