Let be a binary form with integer coefficients, non-zero discriminant and degree with at least and let denote the largest degree of an irreducible factor of over the rationals. Let be an integer with and suppose that there is no prime such that divides for all pairs of integers . Let denote the number of -free integers of absolute value at most which are represented by . We prove that there is a positive number such that is asymptotic to provided that exceeds or is or .
Cite this article
Cameron L. Stewart, Stanley Yao Xiao, On the representation of -free integers by binary forms. Rev. Mat. Iberoam. 37 (2021), no. 2, pp. 723–748DOI 10.4171/RMI/1213