Results 51 to 60 of about 68,409 (246)
Disproof of the Riemann hypothesis
, 2022 Let Theta be the supremum of the real parts of the zeros of the Riemann zeta function. We demonstrate in this note that Theta=1. This entails the existence of infinitely many zeros of zeta(s) off the critical line Re(s) = 1/2, which disproves the Riemann hypothesis.
openaire +1 more source
Analysis of contact Cauchy–Riemann maps III: Energy, bubbling and Fredholm theory
Bulletin of Mathematical Sciences, 2023 In [Y.-G. Oh and R. Wang, Analysis of contact Cauchy-Riemann maps I: A priori [Formula: see text] estimates and asymptotic convergence, Osaka J. Math. 55(4) (2018) 647–679; Y.-G. Oh and R.
Yong-Geun Oh
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A canonical system of differential equations arising from the Riemann zeta-function [PDF]
, 2016 This paper has two main results, which relate to a criteria for the Riemann hypothesis via the family of functions $\Theta_\omega(z)=\xi(1/2-\omega-iz)/\xi(1/2+\omega-iz)$, where $\omega>0$ is a real parameter and $\xi(s)$ is the Riemann xi-function. The
Suzuki, Masatoshi
core
Large gaps between consecutive zeros of the Riemann zeta-function. II
, 2013 Assuming the Riemann Hypothesis we show that there exist infinitely many consecutive zeros of the Riemann zeta-function whose gaps are greater than 2.9 times the average ...
Bui, H. M.
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Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6425-6446, April 2025.ABSTRACT The well‐posedness results for mild solutions to the fractional neutral stochastic differential system with Rosenblatt process with Hurst index Ĥ∈12,1$$ \hat{H}\in \left(\frac{1}{2},1\right) $$ is discussed in this article. To demonstrate the results, the concept of bounded integral contractors is combined with the stochastic result and ...
Dimplekumar N. Chalishajar +3 more
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Remarks on the Connection of the Riemann Hypothesis to Self-Approximation
ComputationBy the Bagchi theorem, the Riemann hypothesis (all non-trivial zeros lie on the critical line) is equivalent to the self-approximation of the function ζ(s) by shifts ζ(s+iτ).
Antanas Laurinčikas
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Prime numbers with a certain extremal type property
Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, 2019 The convex hull of the subgraph of the prime counting function x → π(x) is a convex set, bounded from above by a graph of some piecewise affine function x → ε(x). The vertices of this function form an infinite sequence of points (ek,π(ek))1∞.
Edward Tutaj
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Error term of the mean value theorem for binary Egyptian fractions
Open Mathematics, 2020 In this article, the error term of the mean value theorem for binary Egyptian fractions is studied. An error term of prime number theorem type is obtained unconditionally. Under Riemann hypothesis, a power saving can be obtained.
Xiao Xuanxuan, Zhai Wenguang
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An optimal choice of Dirichlet polynomials for the Nyman-Beurling criterion
, 2012 We give a conditional result on the constant in the B\'aez-Duarte reformulation of the Nyman-Beurling criterion for the Riemann Hypothesis. We show that assuming the Riemann hypothesis and that $\sum_{\rho}\frac{1}{|\zeta'(\rho)|^2}\ll T^{3/2-\delta ...
Bettin, Sandro +2 more
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Links between hail hazard and climate modes of variability across Australia
Quarterly Journal of the Royal Meteorological Society, EarlyView.Climate modes of variability influence hail‐prone atmospheric conditions, but links between these drivers and hail hazard across Australia have not been well constrained. We examine relationships between the El Niño Southern Oscillation (ENSO), Indian Ocean Dipole (IOD), and Southern Annular Mode (SAM) and proxy‐derived hail‐prone days across the ...
Quincy F. Tut +2 more
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