Results 21 to 30 of about 73,475 (298)
Mean values of the logarithmic derivative of the Riemann zeta‐function near the critical line [PDF]
Mathematika, 2022 Assuming the Riemann hypothesis and a hypothesis on small gaps between zeta zeros (see equation (ES 2K) below for a precise definition), we prove a conjecture of Bailey, Bettin, Blower, Conrey, Prokhorov, Rubinstein and Snaith [J. Math. Phys.
F. Ge
semanticscholar +1 more source
Lower bounds for negative moments of ζ′(ρ)$\zeta ^{\prime }(\rho )$ [PDF]
Mathematika, 2022 We establish lower bounds for the discrete 2kth moment of the derivative of the Riemann zeta function at nontrivial zeros for all ...
Peng Gao, Liangyi Zhao
semanticscholar +1 more source
Along the Lines of Nonadditive Entropies: q-Prime Numbers and q-Zeta Functions [PDF]
Entropy, 2021 The rich history of prime numbers includes great names such as Euclid, who first analytically studied the prime numbers and proved that there is an infinite number of them, Euler, who introduced the function ζ(s)≡∑n=1∞n−s=∏pprime11−p−s, Gauss, who ...
Ernesto P. Borges +2 more
semanticscholar +1 more source
Comparing the number of ideals in quadratic number fields
Mathematical Modelling and Control, 2022 Denote by $ a_{K}(n) $ the number of integral ideals in $ K $ with norm $ n $, where $ K $ is a algebraic number field of degree $ m $ over the rational field $ \mathcal{Q} $. Let $ p $ be a prime number.
Qian Wang, Xue Han
doaj +1 more source
Journal of Mathematics Research, 2023 We prove the Countably Infinite Subsets of odd primes have cardinality of Arbitrarily Large in Number. This is achieved by demonstrating the asymptotic law of distribution of prime numbers that involves natural logarithm function to be applicable to all ...
John Y. C. Ting
semanticscholar +1 more source
On primeness of the Selberg zeta-function [PDF]
Hokkaido Mathematical Journal, 2020 Comment: To appear in Hokkaido Mathematical ...
GARUNKŠTIS, Ramūnas, STEUDING, Jörn
openaire +4 more sources
Some Observations on the Greatest Prime Factor of an Integer
Annales Mathematicae Silesianae, 2023 We examine the multiplicity of the greatest prime factor in k-full numbers and k-free numbers. We generalize a well-known result on greatest prime factors and obtain formulas related with the Riemann zeta function.
Jakimczuk Rafael
doaj +1 more source
Orbit Growth of Shift Spaces Induced by Bouquet Graphs and Dyck Shifts
Mathematics, 2021 For a discrete dynamical system, the prime orbit and Mertens’ orbit counting functions describe the growth of its closed orbits in a certain way. The asymptotic behaviours of these counting functions can be determined via Artin–Mazur zeta function of the
Azmeer Nordin, Mohd Salmi Md Noorani
doaj +1 more source
Beurling Zeta Functions, Generalised Primes, and Fractal Membranes [PDF]
Acta Applicandae Mathematicae, 2006 We study generalised prime systems $\mathcal{P ...
Hilberdink, Titus W., Lapidus, Michel L.
openaire +3 more sources
The Derivation of the Riemann Analytic Continuation Formula from the Euler’s Quadratic Equation
Journal of Nigerian Society of Physical Sciences, 2022 The analysis of the derivation of the Riemann Analytic Continuation Formula from Euler’s Quadratic Equation is presented in this paper. The connections between the roots of Euler’s quadratic equation and the Analytic Continuation Formula of the Riemann ...
Opeyemi O. Enoch +2 more
doaj +1 more source