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The theta cycles for modular forms modulo prime powers

  • Jigu Kim EMAIL logo und Yoonjin Lee
Veröffentlicht/Copyright: 31. März 2023

Abstract

Recently, Chen and Kiming studied the theta operator on modular forms modulo prime powers p m , where p 5 and m 2 . In this paper, we study mod p m filtrations and mod p m theta cycles. We give a bound on some elements in the mod p m theta cycle ( m 2 ), and we exactly compute those values in the case that m = 2 .

MSC 2020: 11F33; 11F11

Communicated by Jan Bruinier


Award Identifier / Grant number: 2019R1A6A1A11051177

Award Identifier / Grant number: 2020R1I1A1A01074746

Award Identifier / Grant number: NRF-2022R1A2C1003203

Funding statement: The authors were supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (grant no. 2019R1A6A1A11051177). In addition, Jigu Kim was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (grant no. 2020R1I1A1A01074746), and Yoonjin Lee was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (NRF-2022R1A2C1003203).

Acknowledgements

The authors deeply thank the reviewers for constructive comments and suggestions, which was helpful for improving the quality and readability of this paper.

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Received: 2021-11-10
Revised: 2023-01-21
Published Online: 2023-03-31
Published in Print: 2023-05-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 1.11.2025 von https://www.degruyterbrill.com/document/doi/10.1515/forum-2021-0284/html
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