Results 151 to 160 of about 1,611,376 (286)
On the Approximation of the Hardy Z-Function via High-Order Sections
AxiomsThe Z-function is the real function given by Z(t)=eiθ(t)ζ12+it, where ζ(s) is the Riemann zeta function, and θ(t) is the Riemann–Siegel theta function. The function, central to the study of the Riemann hypothesis (RH), has traditionally posed significant
Yochay Jerby
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Environmental Microbiology, Volume 27, Issue 10, October 2025.The aquatic microbiome can influence cyanobacterial harmful algal blooms. Abundances of genes and transcripts for phosphorus acquisition, denitrification and nitrogen fixation were higher upstream, whereas in Lake Erie genes and transcripts for microcystin production were higher.
Sophie Crevecoeur +9 more
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The Effect of the Density of Square-Free ωp-numbers on the Bounds of Beurling Counting Function
Zanco Journal of Pure and Applied SciencesPrimitive weird numbers are weird numbers which are not a multiple of any smaller weird numbers. The goal of this work is to use a square-free primitive weird number x=ab where b be an increasing sequence of prime numbers such that q1 is greater than ∏
Sarah Al-Ebrahimy, Eman F. Mohommed
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European Journal of Neuroscience, Volume 62, Issue 7, October 2025.Can responsiveness to closed‐loop acoustic stimulation (CLAS) be modulated by anodal transcranial direct current stimulation (AmodCLAS) during sleep? Such induced differences in excitability may partially explain variability in CLAS efficacy. AmodCLAS affected offline detected slow oscillations, reduced sleep efficiency, and REM sleep.
T. Hausdorf +5 more
wiley +1 more source
An Equivalent to the Riemann Hypothesis
, 2023 The Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part $\frac{1}{2}$. It is considered by many to be the most important unsolved problem in pure mathematics. There are several statements equivalent to the famous Riemann hypothesis.
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Proof of the Riemann Hypothesis
Background: The non-trivial zeros of the Riemann zeta function govern prime distributions, and the Riemann Hypothesis states that they all lie on the critical line $\operatorname{Re}s=\tfrac12$. Methods: We place a self-adjoint restriction $R_{\mathrm{PW}}$ of the first-order differentiation operator on a weighted Hilbert space $H_\alpha$ and, under ...
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Governance, Volume 38, Issue 4, October 2025.ABSTRACT While pursuing a professional delivery of public services, street‐level bureaucrats increasingly face intense political‐ideological pressure. Yet, preceding scholars have barely explored how they manage to resist it. Addressing this gap, the paper presents a concept of the coping mechanisms street‐level bureaucrats employ to shield their ...
Laurin Friedrich
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, 2012 This paper has been withdrawn by the author due to a crucial error on last page: The choice of the functions F and G does not meet condition 4 of Theorem ...
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Vanishing of Schubert coefficients via the effective Hilbert nullstellensatz
Forum of Mathematics, SigmaSchubert Vanishing is a problem of deciding whether Schubert coefficients are zero. Until this work it was open whether this problem is in the polynomial hierarchy ${{\mathsf {PH}}}$ .
Igor Pak, Colleen Robichaux
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Journal of Sleep Research, Volume 34, Issue 5, October 2025.Summary Insomnia is highly prevalent and associated with serious health issues. Despite the negative impact of poor sleep on mind and body, most people do not seek treatment. This study aimed to examine the strategies used to improve sleep in the general population with a particular focus on music.
Rasmus Møller Buus +2 more
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