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Asymptotic bounds for special values of shifted convolution Dirichlet series


Author: Olivia Beckwith
Journal: Proc. Amer. Math. Soc. 145 (2017), 2373-2381
MSC (2010): Primary 11F67, 11F66, 11M41
DOI: https://doi.org/10.1090/proc/13417
Published electronically: December 9, 2016
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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 \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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Additional Information

Olivia Beckwith
Affiliation: Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322
Email: olivia.dorothea.beckwith@emory.edu

DOI: https://doi.org/10.1090/proc/13417
Received by editor(s): May 18, 2016
Received by editor(s) in revised form: August 1, 2016
Published electronically: December 9, 2016
Communicated by: Kathrin Bringmann
Article copyright: © Copyright 2016 American Mathematical Society