Number of integers represented byfamilies of binary forms (I)
Volume 209 / 2023
Acta Arithmetica 209 (2023), 219-267
MSC: Primary 11E76; Secondary 11D45, 11D85.
DOI: 10.4064/aa220606-16-2
Published online: 7 June 2023
Abstract
We extend our previous results on the number of integers which are values of some cyclotomic form of degree larger than a given value, to more general families of binary forms with integer coefficients. Our main ingredient is an asymptotic upper bound for the cardinality of the set of values which are common to two non-isomorphic binary forms of degree greater than $3$. We apply our results to some typical examples of families of binary forms.
