Results 51 to 60 of about 71,062 (275)

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
semanticscholar   +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

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
semanticscholar   +1 more source

Identities for the Riemann zeta function [PDF]

The Ramanujan Journal, 2011
14 ...
openaire   +3 more sources

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

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, Darius Šiaučiūnas, Gediminas Vadeikis   +2 more
doaj   +1 more source

Large greatest common divisor sums and extreme values of the Riemann zeta function [PDF]

, 2015
It is shown that the maximum of $|\zeta(1/2+it)|$ on the interval $T^{1/2}\le t \le T$ is at least $\exp\left((1/\sqrt{2}+o(1)) \sqrt{\log T \log\log\log T/\log\log T}\right)$.
A. Bondarenko, K. Seip
semanticscholar   +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

An In-Depth Investigation of the Riemann Zeta Function Using Infinite Numbers

Mathematics
This 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

Moments of the Riemann zeta function on short intervals of the critical line [PDF]

Annals of Probability, 2019
We show that as $T\to \infty$, for all $t\in [T,2T]$ outside of a set of measure $\mathrm{o}(T)$, $$ \int_{-(\log T)^{\theta}}^{(\log T)^{\theta}} |\zeta(\tfrac 12 + \mathrm{i} t + \mathrm{i} h)|^{\beta} \mathrm{d} h = (\log T)^{f_{\theta}(\beta ...
L. Arguin, Frédéric Ouimet, Maksym Radziwill   +2 more
semanticscholar   +1 more source