Results 11 to 20 of about 71,062 (275)

On the Riemann zeta function [PDF]

Bulletin of the American Mathematical Society, 1923
C. F. Craig
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Extended Riemann Zeta Functions [PDF]

Rocky Mountain Journal of Mathematics, 2001
Analogous to recent useful generalizations of the family of gamma functions and beta functions, extensions of the Riemann zeta function are presented, for which the usual properties and representations are naturally and simply extended. In analogy to these extensions, the extended Hurwitz functions are introduced. Hurwitz-type formulae are also proved.
M. Aslam Chaudhry, Asghar Qadir, M.T. Boudjelkha, M. Mujahid Rafique, S. M. Zubair   +4 more
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On Maslanka's Representation for the Riemann Zeta Function [PDF]

International Journal of Mathematics and Mathematical Sciences, 2010
A rigorous proof is given of the hypergeometric-like representation of the Riemann zeta function 𝜁(𝑠) discovered by Maslanka as a series of Pochhamer polynomials with coefficients depending on the values of 𝜁 at the positive even integers.
Luis Báez-Duarte
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Quantum spin chains and Riemann zeta function with odd arguments [PDF]

, 2001
Riemann zeta function is an important object of number theory. It was also used for description of disordered systems in statistical mechanics. We show that Riemann zeta function is also useful for the description of integrable model.
H. Boos, V. E. Korepin
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Explicit zero-free regions for the Riemann zeta-function [PDF]

Research in Number Theory, 2022
We prove that the Riemann zeta-function $$\zeta (\sigma + it)$$ ζ ( σ + i t )
Michael J. Mossinghoff, T. Trudgian, Andrew Yang   +2 more
semanticscholar   +1 more source

Shifted moments of the Riemann zeta function [PDF]

Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2022
In this article, we prove that the Riemann hypothesis implies a conjecture of Chandee on shifted moments of the Riemann zeta function. The proof is based on ideas of Harper concerning sharp upper bounds for the $2k$ th moments of the Riemann zeta ...
Nathan Ng, Quanli Shen, PENG-JIE Wong
semanticscholar   +1 more source

Aspects of the screw function corresponding to the Riemann zeta‐function [PDF]

Journal of the London Mathematical Society, 2022
We introduce a screw function corresponding to the Riemann zeta‐function and study its properties from various aspects. Typical results are several equivalent conditions for the Riemann hypothesis in terms of the screw function.
Masatoshi Suzuki
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Maxima of a random model of the Riemann zeta function over intervals of varying length [PDF]

Annales De L Institut Henri Poincare-probabilites Et Statistiques, 2021
We consider a model of the Riemann zeta function on the critical axis and study its maximum over intervals of length $(\log T)^{\theta}$, where $\theta$ is either fixed or tends to zero at a suitable rate.
L. Arguin, Guillaume Dubach, Lisa Hartung   +2 more
semanticscholar   +1 more source

Four Variants of Riemann Zeta Function

Mathematics, 2022
By means of the generating function method and Dougall’s formulae for bilateral hypergeometric series, we examine four classes of infinite series, which may be considered as variants of Riemann zeta function. Several summation formulae are established in
Nadia N. Li, Wenchang Chu
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Accurate estimation of sums over zeros of the Riemann zeta-function [PDF]

Mathematics of Computation, 2020
We consider sums of the form $\sum \phi(\gamma)$, where $\phi$ is a given function, and $\gamma$ ranges over the ordinates of nontrivial zeros of the Riemann zeta-function in a given interval.
R. Brent, Dave Platt, T. Trudgian
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