Relations and positivity results for the derivatives of the Riemann \(\xi\) function.

DOI10.1016/j.cam.2003.09.003zbMath1107.11033OpenAlexW1967463986MaRDI QIDQ1428473

Mark W. Coffey

Publication date: 29 March 2004

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2003.09.003

zbMATH Keywords

Riemann zeta functionRiemann xi functionLi criterionTheta functionDerivativesFunctional equation

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26)

Related Items (17)

New results on the Stieltjes constants: asymptotic and exact evaluation ⋮ The theta-Laguerre calculus formulation of the Li/Keiper constants ⋮ On the log-concavity of a Jacobi theta function ⋮ Polygamma theory, the Li/Keiper constants and the Li criterion for the Riemann hypothesis ⋮ Series representations for the Stieltjes constants ⋮ A NOTE ON AN EQUIVALENT OF THE RIEMANN HYPOTHESIS ⋮ A note on series equivalent of the Riemann hypothesis ⋮ Sharpenings of Li's criterion for the Riemann hypothesis ⋮ On certain sums over the non-trivial zeta zeroes ⋮ Li coefficients for automorphic \(L\)-functions ⋮ The Stieltjes constants, their relation to the ηj coefficients, and representation of the Hurwitz zeta function ⋮ Toward verification of the Riemann hypothesis: application of the Li criterion ⋮ Asymptotic estimation of $\xi ^{(2n)}(1/2)$: On a conjecture of Farmer and Rhoades ⋮ New results concerning power series expansions of the Riemann xi function and the Li/Keiper constants ⋮ An asymptotic form for the Stieltjes constants 𝛾_{𝑘}(𝑎) and for a sum 𝑆ᵧ(𝑛) appearing under the Li criterion ⋮ Expressions for two generalized Furdui series ⋮ Summation properties of the \(\eta _j\) and Li constants

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The signs of some constants associated with the Riemann zeta-function
• A zero-density theorem for the Riemann zeta-function
• The Riemann zeta-function. Transl. from the Russian by Neal Koblitz
• The positivity of a sequence of numbers and the Riemann hypothesis

This page was built for publication: Relations and positivity results for the derivatives of the Riemann \(\xi\) function.