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Laguerre inequalities and complete monotonicity for the Riemann Xi-function and the partition function

, 2023
Larry X. W. Wang, Neil Yang
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On the Way to Riemann’s Entire Function $$\xi (s)$$ξ(s)

2018
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New results concerning power series expansions of the Riemann xi function and the Li/Keiper constants

, 2008
Mark W. Coffey
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Some Results of Derivatives of Reimann Xi Function from Analytical Expression of Riemann Xi Function ξ(s)

, 2021
Debasis Biswas
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Riemann xi function and modified Bessel functions

В. М. Капустин
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Curvature Properties of the Riemann Xi Function

Jon A. Breslaw
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A Tsallis-Modular Spectral Construction of the Riemann Xi Function and the Critical Line

Fredrick Michael
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Analytical Expression of Complex Riemann Xi Function ξ(s) and Proof of Riemann Hypothesis

, 2021
Debasis Biswas
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Zeros of combinations of the Riemann $\Xi$-function and the confluent hypergeometric function on bounded vertical shifts

, 2017
Atul Dixit, Rahul Kumar, Bibekananda Maji, Alexandru Zaharescu   +3 more
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Convexity and the Riemann \(\xi\)-function.

The Riemann hypothesis is known to be equivalent to the statement that all the zeros of the Fourier transform \(H(x)=\int _ 0 ^ {\infty} \Phi (t)\cos (xt)\,dt\) with \[ \Phi (t)=\sum _ {n=1} ^ {\infty} \pi n^2(2\pi n^2e^ {4t}-3)\exp (5t-\pi n^2e^ {4t}) \] are real. Therefore it is of interest to study the kernel \(\Phi (t)\).
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