English

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.

Keywords

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}
}
R2 v1 2026-06-28T04:47:24.734Z