On the prime zeta function and the Riemann hypothesis
, 2019 By considering the prime zeta function, the author intended to demonstrate in that the Riemann zeta function zeta(s) does not vanish for Re(s)>1/2, which would have proven the Riemann hypothesis. However, he later realised that the proof of "Theorem 3" is fundamentally flawed.
Tatenda Kubalalika
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General decay for second-order abstract viscoelastic equation in Hilbert spaces with time delay
Boletim da Sociedade Paranaense de Matemática, 2022 The paper is concerned with a second-order abstract viscoelastic equation with time delay and a relaxation function satisfying $ h^{\prime}(t)\leq -\zeta(t) G(h(t))$.
Houria Chellaoua, Yamna Boukhatem
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Gaps between primes, and the pair correlation of zeros of the zeta-function [PDF]
Acta Arithmetica, 1982 D. R. Heath‐Brown
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Orbit Growth of Periodic-Finite-Type Shifts via Artin–Mazur Zeta Function
Mathematics, 2020 The prime orbit and Mertens’ orbit counting functions describe the growth of closed orbits in a discrete dynamical system in a certain way. In this paper, we prove the asymptotic behavior of these functions for a periodic-finite-type shift.
Azmeer Nordin, Mohd Salmi Md Noorani
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Riemann zeros from Floquet engineering a trapped-ion qubit
npj Quantum Information, 2021 The non-trivial zeros of the Riemann zeta function are central objects in number theory. In particular, they enable one to reproduce the prime numbers. They have also attracted the attention of physicists working in random matrix theory and quantum chaos
Ran He +8 more
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Explicit versions of the prime ideal theorem for Dedekind zeta functions under GRH [PDF]
Mathematics of Computation, 2015 Followed referee's advice including changing ...
Loïc Grenié, Giuseppe Molteni
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Distribution of Beurling primes and zeroes of the Beurling zeta function I. Distribution of the zeroes of the zeta function of Beurling [PDF]
, 2020 We prove three results on the density resp. local density and clustering of zeros of the Beurling zeta function $ζ(s)$ close to the one-line $σ:=\Re s=1$. The analysis here brings about some news, sometimes even for the classical case of the Riemann zeta function.
Szilárd Gy. Révész
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The Astrophysical Journal, 2023 We present the analysis of the magnetic field ( B -field) structure of galaxies measured with far-infrared (FIR) and radio (3 and 6 cm) polarimetric observations.
Alejandro S. Borlaff +15 more
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Zeta functions and asymptotic additive bases with some unusual sets of primes [PDF]
The Ramanujan Journal, 2015 Fix $ \in(0,1]$, $ _0\in[0,1)$ and a real-valued function $\varepsilon(x)$ for which $\limsup_{x\to\infty}\varepsilon(x)\le 0$. For every set of primes ${\mathcal P}$ whose counting function $ _{\mathcal P}(x)$ satisfies an estimate of the form $$ _{\mathcal P}(x)= \, (x)+O\bigl(x^{ _0+\varepsilon(x)}\bigr),$$ we define a zeta function $ _ ...
William D. Banks
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Riemann zeta fractional derivative—functional equation and link with primes [PDF]
Advances in Difference Equations, 2019 Abstract This paper outlines further properties concerning the fractional derivative of the Riemann ζ function. The functional equation, computed by the introduction of the Grünwald–Letnikov fractional derivative, is rewritten in a simplified form that reduces the computational cost.
Emanuel Guariglia, Emanuel Guariglia
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