Polygamma theory, the Li/Keiper constants and the Li criterion for the Riemann hypothesis

DOI10.1216/RMJ-2010-40-6-1841zbMath1226.11085MaRDI QIDQ618664

Mark W. Coffey

Publication date: 17 January 2011

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Riemann zeta functionRiemann hypothesisLi criterionLi/Keiper constants

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Gamma, beta and polygamma functions (33B15) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26)

Related Items (4)

Polygamma theory, the Li/Keiper constants and the Li criterion for the Riemann hypothesis ⋮ On finite sums of Laguerre polynomials ⋮ An asymptotic form for the Stieltjes constants 𝛾_{𝑘}(𝑎) and for a sum 𝑆ᵧ(𝑛) appearing under the Li criterion ⋮ Summation properties of the \(\eta _j\) and Li constants

Cites Work

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• Polygamma theory, the Li/Keiper constants and the Li criterion for the Riemann hypothesis
• New results on the Stieltjes constants: asymptotic and exact evaluation
• Complements to Li's criterion for the Riemann Hypothesis
• The Riemann zeta-function. Transl. from the Russian by Neal Koblitz
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• Relations and positivity results for the derivatives of the Riemann \(\xi\) function.
• On Maslanka's representation for the Riemann zeta function
• Li coefficients for automorphic \(L\)-functions
• Toward verification of the Riemann hypothesis: application of the Li criterion
• New summation relations for the Stieltjes constants
• Power Series Expansions of Riemann's ζ Function
• New results concerning power series expansions of the Riemann xi function and the Li/Keiper constants

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