Asymptotic expansions for the coefficients of extremal quasimodular forms and a conjecture of Kaneko and Koike

Peter Grabner*

*Korrespondierende/r Autor/in für diese Arbeit

Publikation: Beitrag in einer FachzeitschriftArtikel

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.
Originalspracheenglisch
Seitenumfang18
FachzeitschriftThe Ramanujan Journal
DOIs
PublikationsstatusElektronische Veröffentlichung vor Drucklegung. - Feb 2021

ASJC Scopus subject areas

  • !!Algebra and Number Theory

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