Results 81 to 90 of about 1,611,376 (286)
The Complete Proof of the Riemann Hypothesis [PDF]
, 2021 Robin criterion states that the Riemann Hypothesis is true if and only if the inequality $\sigma(n) < e^{\gamma } \times n \times \log \log n$ holds for all $n > 5040$, where $\sigma(n)$ is the sum-of-divisors function and $\gamma \approx 0.57721$ is the Euler-Mascheroni constant.
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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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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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Optimal Control Applications and Methods, EarlyView.The graphical abstract highlights our research on Sobolev Hilfer fractional Volterra‐Fredholm integro‐differential (SHFVFI) control problems for 1<ϱ<2$$ 1<\varrho <2 $$. We begin with the Hilfer fractional derivative (HFD) of order (1,2) in Sobolev type, which leads to Volterra‐Fredholm integro‐differential equations.
Marimuthu Mohan Raja +3 more
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A Proof Of The Riemann Hypothesis
, 2022 I show a proof of the Riemann Hypothesis by proving the truth of Robin's inequality with a generating function approach. I also show that an ordinary generating function for $\ln(\ln(n))n{e}^{\gamma}$, where $n \in \mathbb{N} \backslash\{1\} $, can be achieved by transforming the polylogarithm and its associated Lambert series[3].
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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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Statistical Deferred Weighted Riemann Summability and Fuzzy Approximation Theorems [PDF]
Sahand Communications in Mathematical AnalysisThe notion of statistical convergence has fascinated many researchers due mainly to the fact that it is more general than the well-established hypothesis of ordinary (classical) convergence.
Priyadarsini Parida +2 more
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A modular relation involving non-trivial zeros of the Dedekind zeta function, and the generalized Riemann hypothesis [PDF]
Journal of Mathematical Analysis and Applications, 2022 Atul Dixit, Shiv Gupta, A. Vatwani
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Hilbert-Polya conjecture and Generalized Riemann Hypothesis [PDF]
, 2013 Extending a classical integral representation of Dirichlet L-functions associated to a non trivial primitive character we define associated functions B(y,z) which are eigenfunction of a Hermitian operator H. The eigenvalues are the imaginary parts of the
Barrau, Bertrand
core
Small, EarlyView.This study investigates how strong dipole–dipole coupling in linear chains of synthesized superparamagnetic nanoparticles induces superferromagnetism, enhancing Magnetic Particle Imaging (MPI) resolution. A positive feedback model predicts key magnetic behaviors, such as coercivity, and guides nanoparticle synthesis.
Chinmoy Saayujya +13 more
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