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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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Proteomic and Transcriptomic Signatures of Poor Asthma Symptom Control in the U‐BIOPRED Cohort
Allergy, EarlyView.No stable features were identified as associated with asthma symptom control in transcriptomics or sputum proteomics. Higher TWEAKR/TNFRSF12A and MBL/MBP‐C serum levels increased the odds of uncontrolled symptoms, while higher MK08/MAPK8 and CD5L serum levels decreased the odds, after adjustment for clinical variables.
Joana Antão +294 more
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Equivalents of the Riemann hypothesis involving the Gram points
Mathematical Modelling and AnalysisThe Riemann hypothesis (RH) on zeros of the zeta-function $\zeta(s)$, $s=\sigma +it$, states that all zeros of $\zeta(s)$ in the strip $0< \sigma < 1$ lie on the line $\sigma =1/2$. Several equivalents of RH are known.
Julija Karaliūnaitė +1 more
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New versions of the Nyman-Beurling criterion for the Riemann hypothesis
International Journal of Mathematics and Mathematical Sciences, 2002 Let ρ(x)=x−[x], χ=χ(0,1), λ(x)=χ(x)logx, and M(x)=ΣK≤x μ(k), where μ is the Möbius function.
Luis Báez-Duarte
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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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Clinical Otolaryngology, EarlyView.ABSTRACT Introduction Frontal beak reduction is a critical and challenging step in endoscopic sinus surgery (ESS) for chronic rhinosinusitis (CRS). Traditional high‐speed drills can risk thermal injury and soft tissue trauma, whereas piezoelectric surgery uses ultrasonic vibrations for selective bone cutting and may improve surgical precision.
Łukasz Skrzypiec +4 more
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An investigation of the non-trivial zeros of the Riemann zeta function
, 2020 The zeros of the Riemann zeta function outside the critical strip are the so-called trivial zeros. While many zeros of the Riemann zeta function are located on the critical line $\Re(s)=1/2$, the non-existence of zeros in the remaining part of the ...
Heymann, Yuri
core
Journal of Child Psychology and Psychiatry, EarlyView.Background From a functionalist perspective, parenting behaviors have adaptive functions and are partly expressions of genetic variation. Maternal genes that have effects on children are often referred to as indirect maternal genetic effects. Indirect genetic effects provide a means for measuring the role of parenting without the need for specifying ...
Espen Moen Eilertsen +8 more
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