Relation between a mock modular form and its shadow through limit values
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- by Dohoon Choi and Subong Lim;
- Proc. Amer. Math. Soc. 153 (2025), 2407-2417
- DOI: https://doi.org/10.1090/proc/17164
- Published electronically: March 24, 2025
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Abstract:
In his last letter to Hardy, Ramanujan defined 17 mock theta functions, and Zwegers discovered that they are holomorphic parts of harmonic weak Maass forms of weight $\frac 12$. Zagier defined a mock modular form as the holomorphic part of a harmonic weak Maass form $F$. The nonholomorphic part of $F$ can be obtained by the nonholomorphic Eichler integral of a cusp form, which is called the shadow. In this paper, we study the relation between a mock modular form and its shadow through limit values of a mock modular form when a mock modular form has weight $k\in \frac 12\mathbb {Z}$ such that $k\leq -2$.References
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Bibliographic Information
- Dohoon Choi
- Affiliation: Department of Mathematics, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, Republic of Korea
- MR Author ID: 784974
- Email: dohoonchoi@korea.ac.kr
- Subong Lim
- Affiliation: Department of Mathematics Education, Sungkyunkwan University, Jongno-gu, Seoul 03063, Republic of Korea
- MR Author ID: 893084
- ORCID: 0000-0003-2768-6172
- Email: subong@skku.edu
- Received by editor(s): July 19, 2024
- Received by editor(s) in revised form: November 4, 2024, and December 5, 2024
- Published electronically: March 24, 2025
- Additional Notes: This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT)(RS-2024-00334203). The first author was supported by a Korea University Grant.
- Communicated by: Amanda Folsom
- © Copyright 2025 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 153 (2025), 2407-2417
- MSC (2020): Primary 11F11, 11F67
- DOI: https://doi.org/10.1090/proc/17164
- MathSciNet review: 4892616