Results 21 to 30 of about 30,359 (214)
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
Odd logarithmic moments of the Riemann zeta-function
Lietuvos Matematikos Rinkinys, 1999 There is not abstract.
Antanas Laurinčikas
doaj +3 more sources
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
doaj +1 more source
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
doaj +1 more source
On Balazard, Saias, and Yor's equivalence to the Riemann Hypothesis
, 2013 Balazard, Saias, and Yor proved that the Riemann Hypothesis is equivalent to a certain weighted integral of the logarithm of the Riemann zeta-function along the critical line equaling zero.
Bui, H. M. +2 more
core +1 more source
Weighted discrete universality of the Riemann zeta-function
Mathematical Modelling and Analysis, 2020 It is well known that the Riemann zeta-function is universal in the Voronin sense, i.e., its shifts ζ(s + iτ), τ ∈ R, approximate a wide class of analytic functions. The universality of ζ(s) is called discrete if τ take values from a certain discrete set.
Antanas Laurinčikas +2 more
doaj +1 more source