Results 41 to 50 of about 72,493 (237)
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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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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AN UPPER BOUND FOR DISCRETE MOMENTS OF THE DERIVATIVE OF THE RIEMANN ZETA‐FUNCTION [PDF]
Mathematika, 2018 Assuming the Riemann hypothesis, we establish an upper bound for the $2k$-th discrete moment of the derivative of the Riemann zeta-function at nontrivial zeros, where $k$ is a positive real number.
S. Kirila
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Matrix model for Riemann zeta via its local factors
Nuclear Physics B, 2020 We propose the construction of an ensemble of unitary random matrices (UMM) for the Riemann zeta function. Our approach to this problem is ‘p-iecemeal’, in the sense that we consider each factor in the Euler product representation of the zeta function to
Arghya Chattopadhyay +3 more
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The Riemann zeta function and Gaussian multiplicative chaos: Statistics on the critical line [PDF]
Annals of Probability, 2016 We prove that if $\omega$ is uniformly distributed on $[0,1]$, then as $T\to\infty$, $t\mapsto \zeta(i\omega T+it+1/2)$ converges to a non-trivial random generalized function, which in turn is identified as a product of a very well behaved random smooth ...
E. Saksman, Christian Webb
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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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An In-Depth Investigation of the Riemann Zeta Function Using Infinite Numbers
MathematicsThis study focuses on an in-depth investigation of the Riemann zeta function. For this purpose, infinite numbers and rotational infinite numbers, which have been introduced in previous studies published by the author, are used.
Emmanuel Thalassinakis
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Approximation of Analytic Functions by Shifts of Certain Compositions
Mathematics, 2021 In the paper, we obtain universality theorems for compositions of some classes of operators in multidimensional space of analytic functions with a collection of periodic zeta-functions.
Darius Šiaučiūnas +2 more
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