On Uniform Approximations of Normal Distributions By Jacobi Theta Functions

TL;DR

This paper investigates how Jacobi theta functions can be used to uniformly approximate normal distributions, demonstrating that scaled theta functions converge exponentially quickly to the normal distribution.

Contribution

It provides a new method for approximating normal distributions using Jacobi theta functions with exponential convergence rates.

Findings

Scaled theta functions approximate the normal distribution exponentially fast.

The approximation method offers a potentially efficient alternative to classical approaches.

Convergence properties are rigorously analyzed and established.

Abstract

In this short note we study uniform approximations to the normal distributions by Jacobi theta functions. We shall show that scaled theta functions approach to a normal distribution exponentially fast.