On the Asymptotics and Distribution of Values of the Jacobi Theta Functions and the Estimate of the Type of the Weierstrass Sigma Functions

Abstract

A refined asymptotics of the Jacobi theta functions and their logarithmic derivatives have been received. The asymptotics of the Nevanlinna characteristics of the indicated functions and the arbitrary elliptic function have been found. The estimation of the type of the Weierstrass sigma functions has been given.

Keywords

• Weierstrass function
• Jacobi theta functions
• Nevanlinna characteristics
• elliptic function
• entire function
• meromorphic function