On a conjecture for representations of integers as sums of squares and double shuffle relations

TL;DR

This paper proves a conjecture regarding the number of representations of integers as sums of eight squares, utilizing advanced theorems and double shuffle relations in the context of modular forms.

Contribution

It provides a proof of a conjecture by Chan and Chua using double Eisenstein series and double shuffle relations, advancing understanding in number theory.

Findings

Confirmed the conjecture for sums of eight squares

Connected double Eisenstein series with representation counts

Applied theorems of Imamoğlu and Kohnen in the proof

Abstract

In this paper, we prove a conjecture of Chan and Chua for the number of representations of integers as sums of 8s integral squares. The proof uses a theorem of Imamo\={g}lu and Kohnen, and the double shuffle relations satisfied by the double Eisenstein series of level 2.