Sur la représentation des entiers par les formes cyclotomiques de grand degré

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 $\phi (n)\ge d$. 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.

25 pages. En français