Automorphic Forms and Holomorphic Functions on the Upper Half-plane
Complex Variables
2022-11-01 v1
Abstract
We define a set of holomorphic functions in terms of the Hauptmodul of a quotient Riemann surface and prove that these functions are holomorphic on the upper half-plane. It is also shown that these functions are automorphic forms of weight k with respect to a Fuchsian group.
Cite
@article{arxiv.2210.16806,
title = {Automorphic Forms and Holomorphic Functions on the Upper Half-plane},
author = {Md. Shafiul Alam},
journal= {arXiv preprint arXiv:2210.16806},
year = {2022}
}