Lower estimates related to the twisted Dedekind function-Reference-Cited by-同舟云学术

Lower estimates related to the twisted Dedekind function

Published:2016-09-06 Issue:07 Volume:12 Page:1801-1811
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Kaczorowski Jerzy¹²,Wiertelak Kazimierz¹

Affiliation:

1. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, 61-614 Poznań, Poland

2. Institute of Mathematics of the Polish Academy of Sciences, 00-956 Warsaw, Poland

Abstract

Let [Formula: see text] be a Dirichlet character. The main goal of this paper is to study oscillations of the difference [Formula: see text] where [Formula: see text] denotes the twisted Dedekind function. We prove that for infinitely many odd characters [Formula: see text] called “good”, we have [Formula: see text], and [Formula: see text] when [Formula: see text] is real. We give a necessary and sufficient condition for [Formula: see text] to be good, and in particular we prove that all odd primitive characters are good. We show also that there are infinitely many moduli [Formula: see text], including all prime powers [Formula: see text], for which all odd characters [Formula: see text] are good.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042116501116

Reference8 articles.

1. Oscillations of the remainder term related to the Euler totient function

2. ON THE SUM OF THE TWISTED EULER FUNCTION

3. Omega theorems related to the general Euler totient function

4. Formulae for the relative class number of an imaginary abelian field in the form of a determinant