Asymptotic bounds for special values of shifted convolution Dirichlet series

Beckwith, Olivia

doi:10.1090/proc/13417

Asymptotic bounds for special values of shifted convolution Dirichlet series
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by Olivia Beckwith PDF

Proc. Amer. Math. Soc. 145 (2017), 2373-2381 Request permission

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 $h \to \infty$. 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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