Results 41 to 50 of about 5,257,133 (195)
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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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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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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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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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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Extended Riemann Zeta Functions
Rocky Mountain Journal of Mathematics, 2001 In this paper two extensions of the Riemann zeta-function are presented. Denoting the real part of the complex variable \(s\) by \(\sigma\), these extensions are \[ \zeta_{b}(s) = {1\over \Gamma(s)}\int_{0}^{\infty}t^{s-1}(e^{t}-1)^{-1}e^{-b/t} dt \quad \quad (b>0; b=0, \sigma >1), \] and \[ \zeta_{b}^{*}(s) = {1\over \Gamma(s)(1-2^{1-s})}\int_{0 ...
Chaudhry, M. Aslam +4 more
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QUANTIZATION OF THE RIEMANN ZETA-FUNCTION AND COSMOLOGY [PDF]
International Journal of Geometric Methods in Modern Physics, 2007 Quantization of the Riemann zeta-function is proposed. We treat the Riemann zeta-function as a symbol of a pseudodifferential operator and study the corresponding classical and quantum field theories. This approach is motivated by the theory of p-adic strings and by recent works on stringy cosmological models.
Aref'eva, I. Ya, Volovich, I. V.
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Notes on the Riemann zeta-function-IV [PDF]
Hardy-Ramanujan Journal, 2000 In earlier papers of this series III and IV, poles of certain meromorphic functions involving Riemann's zeta-function at shifted arguments and Dirichlet polynomials were studied. The functions in question were quotients of products of such functions, and it was shown that they have ``many'' poles.
Balasubramanian, R. +3 more
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Odd logarithmic moments of the Riemann zeta-function
Lietuvos Matematikos Rinkinys, 1999 There is not abstract.
Antanas Laurinčikas
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Hamiltonian for the Zeros of the Riemann Zeta Function [PDF]
Physical Review Letters, 2017 5 pages, version to appear in Phys.
Brody, DC, Bender, CM, Müller, MP
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