# Theta sums of higher index

## TL;DR

This paper investigates the behavior of higher index theta sums within the context of the Schroedinger-Weil representation of the Jacobi group, focusing on positive definite symmetric matrices.

## Contribution

It provides new insights into the properties of higher index theta sums related to the Jacobi group and Schroedinger-Weil representation.

## Key findings

- Characterization of theta sums behavior for higher indices
- Connections between theta sums and the Jacobi group representations
- Potential applications to number theory and harmonic analysis

## Abstract

In this paper, we obtain some behaviours of theta sums of higher index for the Schroedinger-Weil representation of the Jacobi group associated with a positive definite symmetric real matrix of degree m.