Mean values and moments of arithmetic functions over number fields

Jaitra Chattopadhyay, Pranendu Darbar

Published 2018-10-09Version 1

For an odd integer $d \geq 1$ and a finite Galois extension $K/\mathbb{Q}$ of degree $d$, G. L\"{u} and Z. Yang obtained in \cite{lu3} an asymptotic formula for the mean values of the divisor function for $K$ over square integers. In this article, we obtain the same for finitely many number fields of odd degree and pairwise coprime discriminants together with the moment of the error term arising here, following the method adopted by S. Shi in \cite{shi}. We also define the sum of divisor function over number fields and find the asymptotic behaviour of the summatory function of two number fields taken together.