Conjectures of Sun about sums of polygonal numbers

DOI10.1007/S44007-022-00030-1zbMath1508.11044arXiv2109.14793WikidataQ123010157 ScholiaQ123010157MaRDI QIDQ6378984

Kathrin Bringmann, Ben Kane

Publication date: 29 September 2021

Abstract: In this paper, we show that certain sums of generalized $m$-gonal numbers represent every positive integer if and only if they represent every positive integer up to an explicit bound $C_m$, verifying a conjecture of Sun for sufficiently large positive integers.

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Theta series; Weil representation; theta correspondences (11F27) Quadratic forms over global rings and fields (11E12)

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