Results 41 to 50 of about 75,204 (223)

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, Zine El-Abidine Guennoun   +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, Manoj Sahni, Ritu Sahni, Ernesto León-Castro, Maricruz Olazabal-Lugo   +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

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, A Bovier, A Bovier, B Derrida, B Derrida, B Duplantier, CM Newman, CM Newman, CM Newman, D Schumayer, E Bolthausen, E Titchmarsh, F Ouimet, F Ouimet, K Soundararajan, LP Arguin, LP Arguin, LP Arguin, LP Arguin, LP Arguin, LP Arguin, M Biskup, M Radizwiłł, O Daviaud, P Bourgade, P Carmona, Y Saouter, YV Fyodorov   +27 more
core   +1 more source

Multiple finite Riemann zeta functions

, 2004
Observing a multiple version of the divisor function we introduce a new zeta function which we call a multiple finite Riemann zeta function. We utilize some $q$-series identity for proving the zeta function has an Euler product and then, describe the ...
Kimoto, K., Kurokawa, N., Matsumoto, S., Wakayama, M.   +3 more
core   +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, Parikshit Dutta, Suvankar Dutta, Debashis Ghoshal   +3 more
doaj   +1 more source

Theta and Riemann xi function representations from harmonic oscillator eigensolutions

, 2006
From eigensolutions of the harmonic oscillator or Kepler-Coulomb Hamiltonian we extend the functional equation for the Riemann zeta function and develop integral representations for the Riemann xi function that is the completed classical zeta function. A
Abramowitz, Andrews, Atakishiyeva, Bump, Bump, Cartier, Coffey, Coffey, Coffey, Dykman, Edwards, Freilikher, Gradshteyn, Horikis, Keating, Kostelecký, Kurlberg, Lambert, Lebedev, Mark W. Coffey, Mehta, Nieto, Nieto, Platzman, Titchmarsh, Weyl   +25 more
core   +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, Raivydas Šimėnas, Monika Tekorė   +2 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