Abstract
Let F be a binary form with integer coefficients, non-zero discriminant and degree d with d at least 3. Let \(R_F(Z)\) denote the number of integers of absolute value at most Z which are represented by F. We prove that there is a positive number \(C_F\) such that \(R_F(Z)\) is asymptotic to \(C_F Z^{\frac{2}{d}}\).
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Communicated by Kannan Soundararajan.
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The research of the first author was supported in part by the Canada Research Chairs Program and by Grant A3528 from the Natural Sciences and Engineering Research Council of Canada.
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Stewart, C.L., Xiao, S.Y. On the representation of integers by binary forms. Math. Ann. 375, 133–163 (2019). https://doi.org/10.1007/s00208-019-01855-y
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DOI: https://doi.org/10.1007/s00208-019-01855-y