On representations of positive integers by (a+c)^1/3x + (b+d)y, (a+c)x + (k(b+d) )^1/3 y, and (k(a+c) )^1/3 x + l(b+d) y

2012/10/13 by Mohamed El Bachraoui, Bachraoui, Mohamed El
Mathematics · #11A25 #Analytic Number Theory Research #Benford’s Law and Fraud Detection #FOS: Mathematics #Mathematical Approximation and Integration #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1210.3708

openalex publication_date 2012/10/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We use sums of Liouville type to count the number of ways a positive integer can be represented by the forms (a+c)^1/3x + (b+d)y, (a+c)x + (k(b+d) )^1/3 y, and (k(a+c) )^1/3 x + l(b+d) y for nonnegative integers a,b,c,d,k,l,x,y under certain relative primality conditions.

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