A new proof of the transformation law of Jacobi’s theta function $\theta _3(w,\tau )$
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- by Wissam Raji PDF
- Proc. Amer. Math. Soc. 135 (2007), 3127-3132 Request permission
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.References
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Additional Information
- Wissam Raji
- Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
- Email: wissam@temple.edu
- 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
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 3127-3132
- MSC (2000): Primary 11F11, 11F99
- DOI: https://doi.org/10.1090/S0002-9939-07-08867-3
- MathSciNet review: 2322742