On the representation of integers by binary forms

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 $C_F{Z}^{\frac{2}{d}}$.

26 pages, revised version

Cited by in corpus (3)

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