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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A new proof of the transformation law of Jacobi's theta function $ \theta_3(w,\tau)$


Author: Wissam Raji
Journal: Proc. Amer. Math. Soc. 135 (2007), 3127-3132
MSC (2000): Primary 11F11, 11F99
Published electronically: June 21, 2007
MathSciNet review: 2322742
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Abstract: We present a new proof, using Residue Calculus, of the transformation law of the Jacobi theta function $ \theta_3(w,\tau)$ defined in the upper half plane. Our proof is inspired by Siegel's proof of the transformation law of the Dedekind eta function.


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Additional Information

Wissam Raji
Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
Email: wissam@temple.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08867-3
PII: S 0002-9939(07)08867-3
Keywords: Jacobi theta function, Dedekind eta function, Arzela bounded convergence theorem.
Received by editor(s): February 2, 2006
Received by editor(s) in revised form: July 14, 2006, July 24, 2006, and July 28, 2006
Published electronically: June 21, 2007
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2007 American Mathematical Society