Automorphic Forms and Holomorphic Functions on the Upper Half-plane

Md. Shafiul Alam

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arXiv · 2210.16806

Automorphic Forms and Holomorphic Functions on the Upper Half-plane

Md. Shafiul Alam

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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.

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Md. Shafiul Alam. 2022-10-30. Automorphic Forms and Holomorphic Functions on the Upper Half-plane. https://arxiv.org/abs/2210.16806

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