THE ARCSINE LAW ON DIVISORS IN ARITHMETIC PROGRESSIONS MODULAR PRIME POWERS
Résumé
Let x → ∞ be a parameter. In 2016, Feng proved that Deshouillers-Dress-Tenenbaum's arcsine law on divisors of the integers less than x also holds in arithmetic progressions for non Siegel 'exceptional' modulus q exp{(1 4 − ε)(log 2 x) 2 }, where ε is an arbitrarily small positive number. In this paper, we shall show that in the case of prime-power modulus (q := p with p a fixed odd prime and ∈ N) the arcsine law on divisors holds in arithmetic progressions for q x 15/52−ε. 2010 Mathematics Subject Classification. 11N37.
Domaines
Théorie des nombres [math.NT]
Origine : Fichiers produits par l'(les) auteur(s)