Note on the truncated generalizations of Gauss' square exponent theorem

TL;DR

This paper explores extensions of Gauss' square exponent theorem by investigating truncated versions and proposing potential multiple summation generalizations, expanding the theorem's applicability.

Contribution

It introduces new truncations of Gauss' square exponent theorem and discusses possible multiple summation extensions, advancing the theoretical understanding.

Findings

Derived additional truncations of Gauss' square exponent theorem

Proposed potential multiple summation extensions of Liu's results

Enhanced the theoretical framework of the theorem

Abstract

In this note, we investigate J.-C. Liu's work on truncated Gauss' square exponent theorem and obtain more truncations. We also discuss some possible multiple summation extensions of Liu's results.