A formula for Fourier coefficients of certain eta-quotients and their expansions as Eisenstein series

2024/08/18 by Xiaojie Zhu, Zhu, Xiao-Jie
Mathematics · #11F11 #11F30 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Primary 11F20 #Secondary 11F25

paper · pdf · doi:10.48550/arxiv.2408.09480

openalex publication_date 2024/08/18 · openalex created_date 2024/09/13 · openalex updated_date 2026/07/28

Abstract

We give a list of 113 holomorphic eta-quotients of integral weight (66 of which are primitive) and provide a uniform closed formula for their Fourier coefficients c(l) where l≡1\bmodm with some fixed m|24. The proof involves Wohlfahrt's extension of Hecke operators and a dimension formula for spaces of modular forms of general multiplier system. We further provide the expansions of these eta-quotients as linear combinations of standard Eisenstein series.

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