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Level aspect of simultaneous nonvanishing for the central $ L$-values associated to cusp forms


Author: Balesh Kumar
Journal: Proc. Amer. Math. Soc. 148 (2020), 979-991
MSC (2010): Primary 11F11, 11F37, 11F50, 11F67
DOI: https://doi.org/10.1090/proc/14773
Published electronically: October 18, 2019
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Abstract: In this article, we prove a quantitative result on simultaneous nonvanishing of central $ L$-values twisted by quadratic characters for two holomorphic primitive forms with large prime level. We also extend a result of Kohnen to certain higher level forms.


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Additional Information

Balesh Kumar
Affiliation: The Institute of Mathematical Sciences, HBNI, IV Cross Road, CIT Campus, Taramani, Chennai - 600113, India
Address at time of publication: School of Mathematical Sciences, National Institute of Science Education and Research Bhubaneswar, HBNI, P. O. Jatni, Khurda, 752050, Odisha, India
Email: baleshmaths@gmail.com; baleshkumar@niser.ac.in

DOI: https://doi.org/10.1090/proc/14773
Keywords: Jacobi forms, Eichler-Zagier and Shimura correspondences, Waldspurger formula, central $L$-values, quadratic twists
Received by editor(s): March 12, 2019
Received by editor(s) in revised form: June 24, 2019, and July 7, 2019
Published electronically: October 18, 2019
Communicated by: Amanda Folsom
Article copyright: © Copyright 2019 American Mathematical Society