Asymptotic bounds for special values of shifted convolution Dirichlet series
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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.References
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Additional Information
- Olivia Beckwith
- Affiliation: Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322
- MR Author ID: 936383
- Email: olivia.dorothea.beckwith@emory.edu
- 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
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 2373-2381
- MSC (2010): Primary 11F67, 11F66, 11M41
- DOI: https://doi.org/10.1090/proc/13417
- MathSciNet review: 3626496