Some mathematical remarks on the polynomial selection in NFS
Some mathematical remarks on the polynomial selection in NFS
In this work, we consider the proportion of friable (free of large prime factors) values of a binary form $F(X_1,X_2)\in \mathbf {Z}[X_1,X_2]$. In the particular case of quadratic forms, we give an asymptotic equivalent for this proportion which depends on $F$. This is related to Murphyâs $\alpha$ function, which is …