Maass wave forms, quantum modular forms and Hecke operators

We prove that Cohen’s Maass wave form and Li–Ngo–Rhoades’ Maass wave form are Hecke eigenforms with respect to certain Hecke operators. As a corollary, we find new identities of the p th coefficients of these Maass wave forms in terms of p th root of unity.

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Veröffentlicht in:	Research in the mathematical sciences 2019-01, Vol.6 (1), p.1-18, Article 7
1. Verfasser:	Lee, Seewoo
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications of Mathematics Computational Mathematics and Numerical Analysis Mathematics Mathematics and Statistics Modular Forms are Everywhere: Celebration of Don Zagier’s 65th Birthday Operators
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Beschreibung
Zusammenfassung:	We prove that Cohen’s Maass wave form and Li–Ngo–Rhoades’ Maass wave form are Hecke eigenforms with respect to certain Hecke operators. As a corollary, we find new identities of the p th coefficients of these Maass wave forms in terms of p th root of unity.
ISSN:	2522-0144 2197-9847
DOI:	10.1007/s40687-018-0170-0