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May 2008 A Transformation Law of an Eta Product and the Invariance of a Class of Entire Modular Functions Under $\Gamma _0 (n)$
Wissam Raji, Jose Gimenez
Missouri J. Math. Sci. 20(2): 102-114 (May 2008). DOI: 10.35834/mjms/1316032811

Abstract

We present a new proof, using Residue Calculus, of the transformation law of a general eta product under $\Gamma_0(n)$ where $n$ is any integer, then we deduce the invariance of a special case of this product under this group and we prove the transformation law of another special case. Our proof is inspired by Siegel's proof [7] of the transformation law of the Dedekind eta function and by Rademacher's generalization [5].

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Wissam Raji. Jose Gimenez. "A Transformation Law of an Eta Product and the Invariance of a Class of Entire Modular Functions Under $\Gamma _0 (n)$." Missouri J. Math. Sci. 20 (2) 102 - 114, May 2008. https://doi.org/10.35834/mjms/1316032811

Information

Published: May 2008
First available in Project Euclid: 14 September 2011

zbMATH: 1144.11033
Digital Object Identifier: 10.35834/mjms/1316032811

Subjects:
Primary: 11F11
Secondary: 11F20

Rights: Copyright © 2008 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.20 • No. 2 • May 2008
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