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SUMMARY:Glenn T. Bruda (University of Florida)
DTSTART:20260718T200000Z
DTEND:20260718T202500Z
DTSTAMP:20260710T111703Z
UID:CANT2026/91
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2026/91/
 ">Generalized polygonal number representations</a>\nby Glenn T. Bruda (Uni
 versity of Florida) as part of Combinatorial and additive number theory se
 minar (CANT 2026)\n\nLecture held in Science Center in the CUNY Graduate C
 enter (4th floor).\n\nAbstract\nFor $k\\geq5$ and $n\\geq 4$\, let $r_n^{(
 k)}(N)$ be the number of representations of $N$ as the sum of $n$ generali
 zed $k$-gonal numbers and $r_n^{\\square}(N)$ be the number of representat
 ions of $N$ as the sum of $n$ squares. By modifying the Heath-Brown circle
  method\, we prove a closed-form asymptotic relation between $r_{n}^{(k)}(
 N)$ and $r_n^{\\square}(N)$ for $k\\not\\equiv 0\\bmod 4$ and any $n\\geq4
 $. Consequently\, we relate the number of representations of $N$ as the su
 m of four ordinary $k$-gonal numbers to $r_4^{\\square}(N)$ via a result o
 f Bringmann--Jang--Kane--Tse.\n
LOCATION:https://researchseminars.org/talk/CANT2026/91/
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