Some new properties of Jacobi's theta functions

TL;DR

This paper proves a new monotonicity property of the quotient of two Jacobi's theta functions as a function of the modulus, contributing to the understanding of their mathematical behavior.

Contribution

It introduces a novel monotonicity property for the quotient of Jacobi's theta functions with respect to the modulus.

Findings

Established a monotonicity property for the quotient of Jacobi's theta functions.

Provides insights into the behavior of theta functions as the modulus varies.

Enhances theoretical understanding of special functions in complex analysis.

Abstract

In this paper, a monotonicity property for the quotient of two Jacobi's theta functions with respect to the modulus $k$ is proved.