Some conditional results involving arithmetic functions

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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor dc:publisher

University of Missouri--Columbia

Year dc:date.issued

2025

Author dc:creator

• Sinha, Saloni

Advisor dc:contributor.advisor

• Banks, William

Language dc:language.iso

eng, English

DOI

https://doi.org/10.32469/10355/109524

OAI identifier oai:identifier

oai:mospace.umsystem.edu:10355/109524