报告题目：Cooper-Hirschhorn type identities for three or more squares

报告人：唐大钊(重庆师范大学)

报告时间：2024年12月14日（星期六）10:20-11:00

报告地点：数学楼912报告厅

参加人员：本科生、研究生、教师

报告摘要：Let $r_s(n)$ denote the number of representations of $n$ as a sum of $s$ squares. Hurwitz presented eleven cases in which the generating function of $r_s(an+b)$ is a simple infinite product. In 2004, Cooper and Hirschhorn proved that the generating functions of some infinite families of arithmetic sequences in $r_3(n)$ can be expressed as linear combinations of two given generalized eta-quotients. In this talk, we prove that for any $k\geq0$ and $2\leq t\leq50$, the generating functions  $\sum_{n=0}^\infty r_{2t-1}\big(5^{2k+1}n\big)q^n$,

$\sum_{n=0}^\infty r_{2t-1}\big(5^{2k+2}n\big)q^n$ and