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On simultaneous nonvanishing of the central $ L$-values


Author: Wenzhi Luo
Journal: Proc. Amer. Math. Soc. 145 (2017), 4227-4231
MSC (2010): Primary 11F11, 11F37, 11F67
DOI: https://doi.org/10.1090/proc/13572
Published electronically: April 6, 2017
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Abstract: In this note we derive a new quantitative result on the simultaneous nonvanishing of the central $ L$-values twisted by quadratic characters, for pairs of holomorphic cuspidal Hecke eigenforms with large weight $ 2k$.


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Additional Information

Wenzhi Luo
Affiliation: Department of Mathematics, The Ohio State University, Columbus, Ohio 43210
Email: wluo@math.ohio-state.edu

DOI: https://doi.org/10.1090/proc/13572
Keywords: Half-integral weight modular forms, Shimura correspondence, Waldspurger formula, central $L$-values, quadratic twists
Received by editor(s): January 28, 2016
Received by editor(s) in revised form: November 6, 2016
Published electronically: April 6, 2017
Additional Notes: This research was partially supported by NSF grant DMS-1160647
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2017 American Mathematical Society