English

Number of integers represented by families of binary forms

Number Theory 2023-06-06 v3

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 (see \cite{FW1}), 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 33. We apply our results to some typical examples of families of binary forms.

Keywords

Cite

@article{arxiv.2206.03733,
  title  = {Number of integers represented by families of binary forms},
  author = {Étienne Fouvry and Michel Waldschmidt},
  journal= {arXiv preprint arXiv:2206.03733},
  year   = {2023}
}

Comments

Two misprints corrected - the version to appear in Acta Arithmetica is correct