Automorphic Forms and Holomorphic Functions on the Upper Half-plane

Authors

  • Md Shafiul Alam Department of Mathematics, University of Barishal, Barishal-8254, Bangladesh

DOI:

https://doi.org/10.3329/ganit.v43i1.67857

Keywords:

Automorphic form; Holomorphic function; Fuchsian group; Hauptmodul

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.

GANIT J. Bangladesh Math. Soc. 43.1 (2023) 036- 044

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Published

2023-08-02

How to Cite

Alam, M. S. (2023). Automorphic Forms and Holomorphic Functions on the Upper Half-plane. GANIT: Journal of Bangladesh Mathematical Society, 43(1), 036–044. https://doi.org/10.3329/ganit.v43i1.67857

Issue

Vol. 43 No. 1 (2023)

Section

Articles

License

The copyright of GANIT: Journal of Bangladesh Mathematical Society is reserved by Bangladesh Mathematical Society (web: https://bdmathsociety.org/)