Almost Universal Weighted Ternary Sums of Polygonal Numbers

2017/10/16 by Man, Siu Hang, Mehta, Archie
#05A30 #11E20 #11E25 #11E45 #11E81 #11H55 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1710.06023

Abstract

For a natural number m, generalized m-gonal numbers are defined by the formula p_m(x)=((m-2)x²-(m-4)x)/(2) with x∈ \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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