Logarithmic vector-valued modular forms and polynomial-growth estimates of their Fourier coefficients

TL;DR

This paper proves polynomial-growth estimates for Fourier coefficients of holomorphic logarithmic vector-valued modular forms, advancing understanding of their asymptotic behavior.

Contribution

It introduces new polynomial-growth bounds for Fourier coefficients of a specific class of modular forms, expanding theoretical knowledge.

Findings

Established polynomial-growth estimates for Fourier coefficients

Provided bounds applicable to logarithmic vector-valued modular forms

Enhanced understanding of asymptotic behavior of these modular forms

Abstract

We establish (Theorem 3.6) polynomial-growth estimates for the Fourier coefficients of holomorphic logarithmic vector-valued modular forms.