Convexity of Quotients of Theta Functions

Atul Dixit, Arindam Roy, Alexandru Zaharescu

For fixed $u$ and $v$ such that $0\le u<v<1/2$, the monotonicity of the quotients of Jacobi theta functions, namely, ${\theta }_j(u|i\pi t)/{\theta }_j(v|i\pi t)$, $j=1,2,3,4$, on $0<t<\infty$ h…