Transformation formulas of a character analogue of $\log {\theta }_2(z)$

Merve Çelebi Boztaş, Mümün Can

In this paper, transformation formulas for the function \[ A_{1}\left(z,s:χ\right)=\sum\limits_{n=1}^{\infty}\sum\limits_{m=1}^{\infty}χ\left(n\right)χ\left(m\right)\left(-1\right)…