Almost Universal Weighted Ternary Sums of Polygonal Numbers

Siu Hang Man; Archie Mehta

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arXiv · 1710.06023

Almost Universal Weighted Ternary Sums of Polygonal Numbers

Siu Hang Man·Archie Mehta

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Abstract

For a natural number $m$, generalized $m$-gonal numbers are defined by the formula $p_m(x)=\frac{(m-2)x^2-(m-4)x}{2}$ with $x\in \mathbb Z$. In this paper, we determine a criterion on $a,b,c,m$ for which the weighted ternary sum $P_{a,b,c,m}:=ap_m(x)+bp_m(y)+cp_m(z)$ is almost universal. We also prove for some $a,b,c,m$ that the form $P_{a,b,c,m}$ is not almost universal, while it represents all possible congruence classes.

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Siu Hang Man, Archie Mehta. 2017-10-16. Almost Universal Weighted Ternary Sums of Polygonal Numbers. https://arxiv.org/abs/1710.06023

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