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On montre à l’aide de méthodes de crible, de méthodes issues de la théorie des formes automorphes et de géométrie algébrique ainsi qu’à l’aide de la loi de Sato-Tate verticale que le signe des sommes de Kloosterman change une infinité de fois pour parcourant les entiers sans facteur carré ayant au plus facteurs premiers. Ceci améliore un résultat précédent de Fouvry et Michel qui avaient obtenu à la place de .
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