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Mathematics > Number Theory

arXiv:1810.04104 (math)
[Submitted on 9 Oct 2018 (v1), last revised 4 Jun 2019 (this version, v2)]

Title:Mean values and moments of arithmetic functions over number fields

Authors:Jaitra Chattopadhyay, Pranendu Darbar
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Abstract:For an odd integer $d > 1$ and a finite Galois extension $K/\mathbb{Q}$ of degree $d$, G. Lü and Z. Yang \cite{lu3} obtained 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 adapted 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.
Comments: 16 pages. To appear in Res. Number Theory
Subjects: Number Theory (math.NT)
Cite as: arXiv:1810.04104 [math.NT]
  (or arXiv:1810.04104v2 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1810.04104

Submission history

From: Jaitra Chattopadhyay [view email]
[v1] Tue, 9 Oct 2018 16:22:15 UTC (12 KB)
[v2] Tue, 4 Jun 2019 16:01:15 UTC (13 KB)
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