On certain sums of number theory-Reference-Cited by-同舟云学术

On certain sums of number theory

Published:2022-06-24 Issue:09 Volume:18 Page:2053-2074
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Bordellès Olivier¹

Affiliation:

1. 2 Allée de la Combe, 43000 Aiguilhe, France

Abstract

We study sums of the shape [Formula: see text] where [Formula: see text] is either the von Mangoldt function or the Dirichlet–Piltz divisor functions. We improve previous estimates when [Formula: see text] and [Formula: see text], and provide new results when [Formula: see text] with [Formula: see text], breaking the [Formula: see text]-barrier in each case. The functions [Formula: see text], [Formula: see text] and [Formula: see text] are also investigated.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042122501056

Reference14 articles.

1. Sums of two relatively prime cubes

2. On a sum involving the Euler function

3. On a sum involving the number of distinct prime factors function related to the integer part function

4. Decoupling, exponential sums and the Riemann zeta function

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