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dc.contributor.supervisor Akbary, Amir
dc.contributor.author Chalker, Kirsty A.
dc.contributor.author University of Lethbridge. Faculty of Arts and Science
dc.date.accessioned 2019-07-03T16:08:53Z
dc.date.available 2019-07-03T16:08:53Z
dc.date.issued 2019
dc.identifier.uri https://hdl.handle.net/10133/5441
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.language.iso en_US en_US
dc.publisher Lethbridge, Alta. : Universtiy of Lethbridge, Department of Mathematics and Computer 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
dc.publisher.faculty Arts and Science en_US
dc.publisher.department Department of Mathematics and Computer Science en_US
dc.degree.level Masters en_US
dc.proquestyes No en_US
dc.embargo No en_US


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