Abstract
In this paper, we give an asymptotic formula for the proportion of squarefree numbers among \(f_1(x_1)+f_2(x_2)+\cdots +f_s(x_s)\) where \(f_i(x_i)\) is a nonzero cubic polynomial with each \(x_i\) belonging to an interval \([a_iB,b_iB]\), where B tends to infinity. This formula agrees with what has been found in certain cases of single-variable polynomials and binary forms.
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Kowalski, J.M. On the proportion of squarefree numbers among sums of cubic polynomials. Ramanujan J 54, 343–354 (2021). https://doi.org/10.1007/s11139-019-00239-9
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DOI: https://doi.org/10.1007/s11139-019-00239-9