Abstract
Extremal quasimodular forms have been introduced by Kaneko and Koike as quasimodular forms which have maximal possible order of vanishing at i∞. We show an asymptotic formula for the Fourier coefficients of such forms. This formula is then used to show that all but finitely many Fourier coefficients of such forms of depth ≤4 are positive, which partially solves a conjecture stated by Kaneko and Koike. Numerical experiments based on constructive estimates confirm the conjecture for weights ≤200 and depths between 1 and 4.
Original language | English |
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Pages (from-to) | 1021-1041 |
Number of pages | 21 |
Journal | The Ramanujan Journal |
Volume | 57 |
Issue number | 3 |
Early online date | 2022 |
DOIs | |
Publication status | Published - Mar 2022 |
Keywords
- Extremal quasimodular forms
- Fourier coefficients
ASJC Scopus subject areas
- Algebra and Number Theory