A short note on sign changes
Jaban Meher, Karam Deo Shankhadhar, G. K. Viswanadham

TL;DR
This paper provides quantitative results on the number of sign changes in Fourier coefficients of modular forms and generalized modular functions, advancing understanding of their oscillatory behavior.
Contribution
It offers new quantitative bounds on sign changes for Fourier coefficients of Hecke eigenforms and generalized modular functions, extending previous qualitative results.
Findings
Quantitative bounds on sign changes for Fourier coefficients of cusp forms
Results on sign changes of $q$-exponents for generalized modular functions
Extension of sign change analysis to functions on congruence subgroups
Abstract
In this paper, we present a quantitative result for the number of sign changes for the sequences of the Fourier coefficients of normalized Hecke eigen cusp forms for the full modular group . We also prove a similar kind of quantitative result for the number of sign changes of the -exponents of certain generalized modular functions for the congruence subgroup , where is square-free.
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Taxonomy
TopicsAnalytic Number Theory Research · Advanced Algebra and Geometry · Advanced Mathematical Identities
