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Determination of a pair of newforms from the product of their twisted central values

  • Pramath Anamby ORCID logo and Ritwik Pal ORCID logo EMAIL logo
Published/Copyright: November 28, 2024

Abstract

We show that a pair of newforms ( f , g ) can be uniquely determined by the product of the central 𝐿-values of their twists. To achieve our goal, we prove an asymptotic formula for the average of the product of the central values of two twisted 𝐿-functions, L ( 1 / 2 , f × χ ) L ( 1 / 2 , g × χ ψ ) , where ( f , g ) is a pair of newforms. The average is taken over the primitive Dirichlet characters 𝜒 and 𝜓 of distinct prime moduli.

MSC 2020: 11F11; 11F66; 11F67

Award Identifier / Grant number: 0204/14/2022/R&D-II/11126

Award Identifier / Grant number: 0204/31/2021/R&D-II/16488

Funding statement: The authors thank NBHM, DAE for the financial support through NBHM postdoctoral fellowship. The first named author was supported by NBHM grant numbered 0204/14/2022/R&D-II/11126. The second named author was supported by grant numbered 0204/31/2021/R&D-II/16488.

Acknowledgements

The first named author thanks IISER, Pune, where he is a postdoctoral fellow. The second named author thanks ISI, Kolkata, where he is a postdoctoral fellow. The authors thank Ritabrata Munshi for suggesting the problem and for various discussions. The authors also thank Soumya Das for comments and discussions. The authors also thank the anonymous referee for suggestions that made the article better.

  1. Communicated by: Chantal David

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Received: 2023-10-20
Revised: 2024-10-21
Published Online: 2024-11-28
Published in Print: 2025-06-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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