On the Generalization of Radamacher's Proof to $\vartheta_1(z,τ)$
In this paper, we generalize Rademacher's proof of the transformation law of the eta function to the Jacobi theta function using Residue calculus.
math.NT↗
arXiv subjects
Maher Me'meh
Publications and source records attributed to Maher Me'meh.
A generalization of Iseki Formula and the transformation of $\theta_1(z, \tau)$
In this paper we give a generalization of Iseki's formula and use it to prove the transformation law of $\theta_1(z, \tau)$.
math.NT↗
A New Proof For The Transformation Laws of Theta Functions
We prove the transformation laws of the four Jacobi theta functions using Gordon's proof for the transformation law of the Dedekind eta function.
math.NT↗
Generalization of Siegel's Method to theta 1
We present a new proof of the transformation law of $\vartheta_1$ under the action of the generator of the full modular group $\Gamma$ using Siegel's method.
math.CV↗