The theta-Laguerre calculus formulation of the Li/Keiper constants

DOI10.1016/j.jat.2006.10.006zbMath1120.33006OpenAlexW2015947280MaRDI QIDQ2370179

Mark W. Coffey

Publication date: 22 June 2007

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2006.10.006

zbMATH Keywords

Riemann zeta functionRiemann hypothesisLaurent expansionlogarithmic derivativesassociated Laguerre polynomialsRiemann xi functionLi criterionLi/Keiper constantsTheta-Laguerre calculus

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26)

Related Items (6)

On finite sums of Laguerre polynomials ⋮ On certain sums over the non-trivial zeta zeroes ⋮ The Stieltjes constants, their relation to the ηj coefficients, and representation of the Hurwitz zeta function ⋮ 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 ⋮ On the Generalized Li’s Criterion Equivalent to the Riemann Hypothesis and Its First Applications

Cites Work

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• A zero-density theorem for the Riemann zeta-function
• The Riemann zeta-function. Transl. from the Russian by Neal Koblitz
• Weighted permutation problems and Laguerre polynomials
• The positivity of a sequence of numbers and the Riemann hypothesis
• Relations and positivity results for the derivatives of the Riemann \(\xi\) function.
• Toward verification of the Riemann hypothesis: application of the Li criterion
• Properties and possibilities of quantum shapelets
• Power Series Expansions of Riemann's ζ Function
• Positivity Proofs for Linearization and Connection Coefficients of Orthogonal Polynomials Satisfying an Addition Formula
• Random matrix ensembles with an effective extensive external charge
• Partial Characters and Signed Quotient Hypergroups
• Almost periodicity of some error terms in prime number theory
• Cramer functions and Guinand equations
• New results concerning power series expansions of the Riemann xi function and the Li/Keiper constants
• Fourier Reciprocities and the Riemann Zeta-Function

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