Number of integers represented by families of binary forms

Étienne Fouvry; Michel Waldschmidt

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arXiv · 2206.03733

Number of integers represented by families of binary forms

Étienne Fouvry·Michel Waldschmidt

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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 $3$. We apply our results to some typical examples of families of binary forms.

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Étienne Fouvry, Michel Waldschmidt. 2022-06-08. Number of integers represented by families of binary forms. https://arxiv.org/abs/2206.03733

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