Results 61 to 70 of about 552,780 (265)
On two conjectural series involving Riemann zeta function [PDF]
arXiv, 2023 Riemann zeta function is important in a lot of branches of number theory. With the help of the operator method and several transformation formulas for hypergeometric series, we prove four series involving Riemann zeta function. Two of them are series expansions for $\zeta(7)$ and $\zeta(3)^2$ recently conjectured by Z.-W. Sun.
arxiv
Optimizing calibration designs with uncertainty in abilities
British Journal of Mathematical and Statistical Psychology, EarlyView.Abstract Before items can be implemented in a test, the item characteristics need to be calibrated through pretesting. To achieve high‐quality tests, it's crucial to maximize the precision of estimates obtained during item calibration. Higher precision can be attained if calibration items are allocated to examinees based on their individual abilities ...
Jonas Bjermo +2 more
wiley +1 more source
Odd logarithmic moments of the Riemann zeta-function
Lietuvos Matematikos Rinkinys, 1999 There is not abstract.
Antanas Laurinčikas
doaj +1 more source
A Derivation of π(n) Based on a Stability Analysis of the Riemann-Zeta Function [PDF]
, 2010 The prime-number counting function π(n), which is significant in the prime number theorem, is derived by analyzing the region of convergence of the real-part of the Riemann- Zeta function using the unilateral z-transform.
Haranas, Ioannis, Harney, Michael
core +1 more source
Universality of the Riemann zeta-function
Journal of Number Theory, 2010 AbstractIn 1975, S.M. Voronin proved the universality of the Riemann zeta-function ζ(s). This means that every non-vanishing analytic function can be approximated uniformly on compact subsets of the critical strip by shifts ζ(s+iτ). In the paper, we consider the functions F(ζ(s)) which are universal in the Voronin sense.
Antanas Laurinčikas +1 more
openaire +2 more sources
Fractional gaussian noise: Spectral density and estimation methods
Journal of Time Series Analysis, EarlyView.The fractional Brownian motion (fBm) process, governed by a fractional parameter H∈(0,1), is a continuous‐time Gaussian process with its increment being the fractional Gaussian noise (fGn). This article first provides a computationally feasible expression for the spectral density of fGn.
Shuping Shi, Jun Yu, Chen Zhang
wiley +1 more source
Cointegrating Polynomial Regressions With Power Law Trends
Journal of Time Series Analysis, EarlyView.ABSTRACT The common practice in cointegrating polynomial regressions (CPRs) often confines nonlinearities in the variable of interest to stochastic trends, thereby overlooking the possibility that they may be caused by deterministic components. As an extension, we propose univariate and multivariate CPRs that incorporate power law deterministic trends.
Yicong Lin, Hanno Reuvers
wiley +1 more source
Metamaterials and Cesàro convergence
AIP Advances, 2020 In this paper, we show that the linear dielectrics and magnetic materials in matter obey a special kind of mathematical property known as Cesàro convergence.
Yuganand Nellambakam +1 more
doaj +1 more source
The limit of the Riemann zeta function and its nontrivial zeros [PDF]
arXiv, 2019 In this article, with a new approach, which is not discussed in the literature yet, the limit of the Riemann zeta function or Euler-Riemann zeta function is approximately explored by applying Dirichlet's rearrangement theorem for absolutely convergent series to the Riemann zeta function by rearranging its terms as geometric series for sufficiently ...
arxiv
Almost all of the nontrivial zeros of the Riemann zeta-function are on the critical line [PDF]
arXiv, 2022 Applying Littlewood's lemma in connection to Riemann's Hypothesis and exploiting the symmetry of Riemann's $xi$ function we show that almost all nontrivial Riemann's Zeta zeros are on the critical line.
arxiv