Results 31 to 40 of about 552,780 (265)
Some identities related to Riemann zeta-function
Journal of Inequalities and Applications, 2016 It is well known that the Riemann zeta-function ζ ( s ) $\zeta(s)$ plays a very important role in the study of analytic number theory. In this paper, we use the elementary method and some new inequalities to study the computational problem of one kind of
Lin Xin
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Series of Floor and Ceiling Functions—Part II: Infinite Series
Mathematics, 2022 In this part of a series of two papers, we extend the theorems discussed in Part I for infinite series. We then use these theorems to develop distinct novel results involving the Hurwitz zeta function, Riemann zeta function, polylogarithms and Fibonacci ...
Dhairya Shah +4 more
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On the Riemann hypothesis for the zeta function
, 2021 In this paper we address some variants for the products of Hadamard and Patterson. We prove that all zeros of the Riemann $\Xi$--function are real. We also prove that the Riemann hypothesis is true. The equivalence theorems associated with the Riemann zeta--function are obtained in detail.
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Log-tangent integrals and the Riemann zeta function
Mathematical Modelling and Analysis, 2019 We show that integrals involving the log-tangent function, with respect to any square-integrable function on , can be evaluated by the harmonic series. Consequently, several formulas and algebraic properties of the Riemann zeta function at odd positive ...
Lahoucine Elaissaoui +1 more
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Discrete universality for Matsumoto zeta-functions and the nontrivial zeros of the Riemann zeta-function [PDF]
arXiv, 2023 In 2017, Garunk\v{s}tis, Laurin\v{c}ikas and Macaitien\.{e} proved the discrete universality theorem for the Riemann zeta-function sifted by the nontrivial zeros of the Riemann zeta-function. This discrete universality has been extended in various zeta-functions and $L$-functions.
arxiv
A Probabilistic Proof for Representations of the Riemann Zeta Function
Mathematics, 2019 In this paper, we present a different proof of the well known recurrence formula for the Riemann zeta function at positive even integers, the integral representations of the Riemann zeta function at positive integers and at fractional points by means of ...
Jiamei Liu, Yuxia Huang, Chuancun Yin
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Fractional derivative of the Hurwitz ζ-function and chaotic decay to zero
Journal of King Saud University: Science, 2016 In this paper the fractional order derivative of a Dirichlet series, Hurwitz zeta function and Riemann zeta function is explicitly computed using the Caputo fractional derivative in the Ortigueira sense.
C. Cattani, E. Guariglia
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Is the Riemann zeta function in a short interval a 1-RSB spin glass ?
, 2018 Fyodorov, Hiary & Keating established an intriguing connection between the maxima of log-correlated processes and the ones of the Riemann zeta function on a short interval of the critical line.
A Auffinger +27 more
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Identities for the Riemann zeta function [PDF]
The Ramanujan Journal, 2011 We obtain several expansions for $ (s)$ involving a sequence of polynomials in $s$, denoted in this paper by $ _k(s)$. These polynomials can be regarded as a generalization of Stirling numbers of the first kind and our identities extend some series expansions for the zeta function that are known for integer values of $s$.
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Fourier coefficients associated with the Riemann zeta-function
Karpatsʹkì Matematičnì Publìkacìï, 2016 We study the Riemann zeta-function $\zeta(s)$ by a Fourier series method. The summation of $\log|\zeta(s)|$ with the kernel $1/|s|^{6}$ on the critical line $\mathrm{Re}\; s = \frac{1}{2}$ is the main result of our investigation.
Yu.V. Basiuk, S.I. Tarasyuk
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