Some conditional results involving arithmetic functions
Loading...
Authors
Meeting name
Sponsors
Date
Journal Title
Format
Thesis
Subject
Abstract
In analytic number theory, conditional results often serve as a precursor to unconditional results. In this thesis, we present two types of conditional results. First, we establish conditional estimates on twisted sums of certain arithmetic functions such as generalized von Mangoldt and Mobius functions under the Riemann hypothesis, and we also present a strong converse. Second, we investigate a discrete negative moment of the zeta function, obtaining a lower bound that supports a previously conjectured estimate. Both results rely on the use of arithmetic functions and connect to broader problems. While the results we obtain are conditional, they provide a framework that could lead to unconditional estimates through alternative methods.
Table of Contents
DOI
PubMed ID
Degree
Ph. D.