Glenn Bruda

Affiliation: University of Florida

Title Of Talk: Generalized polygonal number representations

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Abstract: For $k\geq5$ and $n\geq4$, let $r_n^{(k)}(N)$ be the number of representations of $N$ as the sum of $n$ generalized $k$-gonal numbers and $r_n^{\square}(N)$ be the number of representations of $N$ as the sum of $n$ squares. By modifying the Heath-Brown circle method, we obtain an explicit asymptotic relation between $r_{n}^{(k)}(N)$ and $r_n^{\square}(N)$. Consequently, we relate the number of representations of $N$ as the sum of four ordinary $k$-gonal numbers to $r_4^{\square}(N)$ via a result of Bringmann--Jang--Kane--Tse.

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