Kaneko and Koike introduced the notion of extremal quasi-modular forms and proposed conjectures on their arithmetic properties. The aim of this paper is to prove a rather sharp multiplicity estimate for these quasi-modular forms. The paper ends with discussions and partial answers around these conjectures and an appendix by G. Nebe containing the proof of the integrality of the Fourier coefficients of the normalized extremal quasi-modular form of weight 14 and depth one.
On extremal quasi-modular forms after kaneko and koike / Pellarin, F.; Nebe, G.. - In: KYUSHU JOURNAL OF MATHEMATICS. - ISSN 1340-6116. - 74:2(2020), pp. 401-413. [10.2206/kyushujm.74.401]
On extremal quasi-modular forms after kaneko and koike
Pellarin F.;
2020
Abstract
Kaneko and Koike introduced the notion of extremal quasi-modular forms and proposed conjectures on their arithmetic properties. The aim of this paper is to prove a rather sharp multiplicity estimate for these quasi-modular forms. The paper ends with discussions and partial answers around these conjectures and an appendix by G. Nebe containing the proof of the integrality of the Fourier coefficients of the normalized extremal quasi-modular form of weight 14 and depth one.| File | Dimensione | Formato | |
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