Perron's formula and resulting explicit bounds on sums
| dc.contributor.author | Chalker, Kirsty A. | |
| dc.contributor.author | University of Lethbridge. Faculty of Arts and Science | |
| dc.contributor.supervisor | Akbary, Amir | |
| dc.date.accessioned | 2019-07-03T16:08:53Z | |
| dc.date.available | 2019-07-03T16:08:53Z | |
| dc.date.issued | 2019 | |
| dc.degree.level | Masters | en_US |
| dc.description.abstract | By working with Perron’s formula we prove an explicit bound on ∑n≤x an/ns, where an,s ∈ C. We then prove a second explicit bound on this sum for the special case where s = 0: These bounds apply to specific sums that are involved in the Prime Number Theorem. Moreover, they are particularly useful in cases where a variant of the Riemann von-Mangoldt explicit formula is not unconditionally available. We choose to implement our bounds on M(x) =∑n≤x μ(n) and m(x) =∑n≤x μ(n/)n (with μ(n) denoting the Möbius function). This gives constants C > 0; c > 0 and x0 > 0 for which |M(x)|≤Cxexp(−c√logx) if x > x0 and a similar kind of bound for m(x): We believe that explicit bounds for M(x) and m(x) like these have never before been published. | en_US |
| dc.embargo | No | en_US |
| dc.identifier.uri | https://hdl.handle.net/10133/5441 | |
| dc.language.iso | en_US | en_US |
| dc.proquestyes | No | en_US |
| dc.publisher | Lethbridge, Alta. : Universtiy of Lethbridge, Department of Mathematics and Computer Science | en_US |
| dc.publisher.department | Department of Mathematics and Computer Science | en_US |
| dc.publisher.faculty | Arts and Science | en_US |
| dc.relation.ispartofseries | Thesis (University of Lethbridge. Faculty of Arts and Science) | en_US |
| dc.subject | Mathematical analysis | en_US |
| dc.subject | Numbers, prime | en_US |
| dc.subject | Number theory | en_US |
| dc.subject | Numbers, complex | en_US |
| dc.subject | Sequences (Mathematics) | en_US |
| dc.subject | Perron's formula | en_US |
| dc.subject | explicit bounds | en_US |
| dc.subject | Prime Number Theorem | en_US |
| dc.subject | sums | en_US |
| dc.subject | Dissertations, Academic | en_US |
| dc.title | Perron's formula and resulting explicit bounds on sums | en_US |
| dc.type | Thesis | en_US |