Asymptotic bounds for special values of shifted convolution Dirichlet series

Olivia Beckwith*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

1 Citation (Scopus)

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 →∞. Our method relies on a result of Mertens and Ono, who showed that these values are Fourier coefficients of mixed mock modular forms.

Original languageEnglish
Pages (from-to)2373-2381
Number of pages9
JournalProceedings of the American Mathematical Society
Volume145
Issue number6
Early online date9 Dec 2016
DOIs
Publication statusPublished - 1 Jan 2017

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