Sectorial Mertens and Mirsky formulae for imaginary quadratic number fields

Formules de Mertens et de Mirsky sectorielles pour des corps quadratiques imaginaires

Jouni Parkkonen (1) , Frédéric Paulin (2)

1 JYU - Department of Mathematics and Statistics [Jyväskylä Univ]
2 LMO - Laboratoire de Mathématiques d'Orsay

We extend formulae of Mertens and Mirsky on the asymptotic behaviour of the standard Euler function to the Euler functions of principal rings of integers of imaginary quadratic number fields, giving versions in angular sectors and with congruences.

Domaines: Théorie des nombres [math.NT]

Jouni Parkkonen, Frédéric Paulin. Sectorial Mertens and Mirsky formulae for imaginary quadratic number fields. 2022. ⟨hal-03683873⟩