Polygamma theory, the Li/Keiper constants, and validity of the Riemann Hypothesis

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dc.creatorCoffey, Mark W.
dc.date2005-07-17
dc.date.accessioned2026-07-07T04:32:13Z
dc.date.available2026-07-07T04:32:13Z
dc.descriptionThe Riemann hypothesis is equivalent to the Li criterion governing a sequence of real constants, that are certain logarithmic derivatives of the Riemann xi function evaluated at unity. We investigate a related set of constants c_n, n = 1,2,..., showing in detail that the leading behaviour (1/2) ln n of lambda_n/n is absent in c_n. Additional results are presented, including a novel explicit representation of c_n in terms of the Stieltjes constants gamma_j. We conjecture as to the large-n behaviour of c_n. Should this conjecture hold, validity of the Riemann hypothesis would follow.
dc.description28 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/math-ph/0507042
dc.identifierhttp://arxiv.org/abs/math-ph/0507042
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58113
dc.subjectMathematical Physics
dc.titlePolygamma theory, the Li/Keiper constants, and validity of the Riemann Hypothesis
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