A New Proof For The Transformation Laws of Theta Functions

2022/07/26 by Me'meh, Maher, Saraeb, Ali
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2207.12806

Abstract

We prove the transformation laws of the four Jacobi theta functions using Gordon's proof for the transformation law of the Dedekind eta function.

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• Transformation Laws for Theta functions
• Self-reciprocal functions, powers of the Riemann zeta function and modular-type transformations
• Theta function identities and q series
• On the Generalization of Radamacher's Proof to ϑ₁(z,τ)
• An Elementary Proof of the Transformation Formula for the Dedekind Eta Function