Abstract

Let $F$ be a binary form with integer coefficients, degree $d\ge 3$ and nonzero discriminant. Let $R_F(Z)$ denote the number of integers of absolute value at most $Z$ which are represented by $F$. In 2019 Stewart and Xiao proved that $R_F(Z)\sim C_F{Z}^{2∕d}$ for some positive number $C_F$. We compute $C_{R_n}$ and $C_{J_n}$ for the binary forms $R_n(x,y)$ and $J_n(x,y)$ defined by means of the relation

where the variables $x$ and $y$ are real.

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