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arXiv · 1909.01892

Sur la repr\'esentation des entiers par les formes cyclotomiques de grand degr\'e

Etienne Fouvry·Michel Waldschmidt
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Abstract

For each integer $d\ge 4$, we study the sequence of positive integers which are represented by one at least of the cyclotomic binary forms $\Phi_n(X,Y)$, with $n$ a positive integer satisfying $\varphi(n)\ge d$. The case $d=2$ was studied in our previous work [FLW]. Our demonstration is based on a variant of a statement of [SX] concerning the common values taken by two binary forms of the same degree and non-zero discriminants. All constants are effectively calculable.

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Etienne Fouvry, Michel Waldschmidt. 2019-09-04. Sur la repr\'esentation des entiers par les formes cyclotomiques de grand degr\'e. https://arxiv.org/abs/1909.01892

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