PreprintCC BY 4.0arXiv
On sign patterns of Fourier coefficients of theta quotients
Abstract
Motivated by conjectures of Schlosser and Zhou on sign patterns of Fourier coefficients of infinite products, we study two families of theta quotients and their positive integral powers. We determine asymptotic formulas for their Fourier coefficients and use them to obtain explicit eventual periodic sign patterns. Our results provide new instances of the sign phenomena observed by Schlosser and Zhou and illustrate how dominant cusps determine the resulting sign patterns. These results were formalized and verified in Lean by AxiomProver.
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BibTeX
@misc{banerjee2026sign,
title = {{On sign patterns of Fourier coefficients of theta quotients}},
author = {Koustav Banerjee and Kathrin Bringmann and Bernhard Heim and Ben Kane},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41569},
eprint = {2610.41569},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41569},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On sign patterns of Fourier coefficients of theta quotients
AU - Koustav Banerjee
AU - Kathrin Bringmann
AU - Bernhard Heim
AU - Ben Kane
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41569
UR - https://arxiv.org/abs/2610.41569
AB - Motivated by conjectures of Schlosser and Zhou on sign patterns of Fourier coefficients of infinite products, we study two families of theta quotients and their positive integral powers. We determine asymptotic formulas for their Fourier coefficients and use them to obtain explicit eventual periodic sign patterns. Our results provide new instances of the sign phenomena observed by Schlosser and Zhou and illustrate how dominant cusps determine the resulting sign patterns. These results were formalized and verified in Lean by AxiomProver.
ER -