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Jinhua Fei - One of the best experts on this subject based on the ideXlab platform.
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Riemann Hypothesis and Value Distribution Theory
viXra, 2020Co-Authors: Jinhua FeiAbstract:Riemann Hypothesis was posed by Riemann in early 50’s of the 19 th century in his thesis titled “The Number of Primes less than a Given Number”. It is one of the unsolved “Supper”problems of mathematics. The Riemann Hypothesis is closely related to the well-known Prime Number Theorem. The Riemann Hypothesis states that all the nontrivial zeros of the zeta-function lie on the ‘critical line’. In this paper, we use Nevanlinna's Second Main Theorem in the value distribution theory, refute the Riemann Hypothesis. In reference [7], we have already given a proof of refute the Riemann Hypothesis, in this paper, we are given out the second proof, please reader reference.
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About The Riemann Hypothesis
viXra, 2020Co-Authors: Jinhua FeiAbstract:The Riemann Hypothesis is part of Hilbert's eighth problem in David Hilbert's list of 23 unsolved problems. it is also one of the Clay Mathematics Institute's Millennium Prize Problems. Some mathematicians consider it the most important unresolved problem in pure mathematics. Many mathematicians made a lot of effort, they don't have to prove the Riemann Hypothesis. In this paper, I use the analytic methods to denied the Riemann Hypothesis, please criticism.
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Riemann Hypothesis and Value Distribution Theory
Journal of Applied Mathematics and Physics, 2017Co-Authors: Jinhua FeiAbstract:Riemann Hypothesis was posed by Riemann in early 50’s of the 19th century in his thesis titled “The Number of Primes less than a Given Number”. It is one of the unsolved “Supper” problems of mathematics. The Riemann Hypothesis is closely related to the well-known Prime Number Theorem. The Riemann Hypothesis states that all the nontrivial zeros of the zeta-function lie on the “critical line” . In this paper, we use Nevanlinna’s Second Main Theorem in the value distribution theory, refute the Riemann Hypothesis. In reference [7], we have already given a proof of refute the Riemann Hypothesis. In this paper, we gave out the second proof, please read the reference.
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About the Riemann Hypothesis
Journal of Applied Mathematics and Physics, 2016Co-Authors: Jinhua FeiAbstract:The Riemann Hypothesis is part of Hilbert’s eighth problem in David Hilbert’s list of 23 unsolved problems. It is also one of the Clay Mathematics Institute’s Millennium Prize Problems. Some mathematicians consider it the most important unresolved problem in pure mathematics. Many mathematicians made a lot of efforts; they don’t have to prove the Riemann Hypothesis. In this paper, I use the analytic methods to deny the Riemann Hypothesis; if there’s something wrong, please criticize and correct me.
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Riemann Hypothesis is Incorrect (Second Proof)
viXra, 2016Co-Authors: Jinhua FeiAbstract:A few years ago, I wrote my paper [4]. In the paper [4], I use Nevanlinna's Second Main Theorem of the value distribution theory, denied the Riemann Hypothesis. In this paper, I use the analytic methods, I once again denied the Riemann Hypothesis
Ambrose Yang - One of the best experts on this subject based on the ideXlab platform.
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Analogues of the Robin–Lagarias criteria for the Riemann Hypothesis
International Journal of Number Theory, 2020Co-Authors: Lawrence C. Washington, Ambrose YangAbstract:Robin’s criterion states that the Riemann Hypothesis is equivalent to [Formula: see text] for all integers [Formula: see text], where [Formula: see text] is the sum of divisors of [Formula: see text] and [Formula: see text] is the Euler–Mascheroni constant. We prove that the Riemann Hypothesis is equivalent to the statement that [Formula: see text] for all odd numbers [Formula: see text]. Lagarias’s criterion for the Riemann Hypothesis states that the Riemann Hypothesis is equivalent to [Formula: see text] for all integers [Formula: see text], where [Formula: see text] is the [Formula: see text]th harmonic number. We establish an analogue to Lagarias’s criterion for the Riemann Hypothesis by creating a new harmonic series [Formula: see text] and demonstrating that the Riemann Hypothesis is equivalent to [Formula: see text] for all odd [Formula: see text]. We prove stronger analogues to Robin’s inequality for odd squarefree numbers. Furthermore, we find a general formula that studies the effect of the prime factorization of [Formula: see text] and its behavior in Robin’s inequality.
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Analogues of the Robin-Lagarias Criteria for the Riemann Hypothesis
arXiv: Number Theory, 2020Co-Authors: Lawrence C. Washington, Ambrose YangAbstract:Robin's criterion states that the Riemann Hypothesis is equivalent to $\sigma(n) < e^\gamma n \log\log n$ for all integers $n \geq 5041$, where $\sigma(n)$ is the sum of divisors of $n$ and $\gamma$ is the Euler-Mascheroni constant. We prove that the Riemann Hypothesis is equivalent to the statement that $\sigma(n) < \frac{e^\gamma}{2} n \log\log n$ for all odd numbers $n \geq 3^4 \cdot 5^3 \cdot 7^2 \cdot 11 \cdots 67$. Lagarias's criterion for the Riemann Hypothesis states that the Riemann Hypothesis is equivalent to $\sigma(n) < H_n + \exp{H_n}\log{H_n}$ for all integers $n \geq 1$, where $H_n$ is the $n$th harmonic number. We establish an analogue to Lagarias's criterion for the Riemann Hypothesis by creating a new harmonic series $H^\prime_n = 2H_n - H_{2n}$ and demonstrating that the Riemann Hypothesis is equivalent to $\sigma(n) \leq \frac{3n}{\log{n}} + \exp{H^\prime_n}\log{H^\prime_n}$ for all odd $n \geq 3$. We prove stronger analogues to Robin's inequality for odd squarefree numbers. Furthermore, we find a general formula that studies the effect of the prime factorization of $n$ and its behavior in Robin's inequality.
Lawrence C. Washington - One of the best experts on this subject based on the ideXlab platform.
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Analogues of the Robin–Lagarias criteria for the Riemann Hypothesis
International Journal of Number Theory, 2020Co-Authors: Lawrence C. Washington, Ambrose YangAbstract:Robin’s criterion states that the Riemann Hypothesis is equivalent to [Formula: see text] for all integers [Formula: see text], where [Formula: see text] is the sum of divisors of [Formula: see text] and [Formula: see text] is the Euler–Mascheroni constant. We prove that the Riemann Hypothesis is equivalent to the statement that [Formula: see text] for all odd numbers [Formula: see text]. Lagarias’s criterion for the Riemann Hypothesis states that the Riemann Hypothesis is equivalent to [Formula: see text] for all integers [Formula: see text], where [Formula: see text] is the [Formula: see text]th harmonic number. We establish an analogue to Lagarias’s criterion for the Riemann Hypothesis by creating a new harmonic series [Formula: see text] and demonstrating that the Riemann Hypothesis is equivalent to [Formula: see text] for all odd [Formula: see text]. We prove stronger analogues to Robin’s inequality for odd squarefree numbers. Furthermore, we find a general formula that studies the effect of the prime factorization of [Formula: see text] and its behavior in Robin’s inequality.
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Analogues of the Robin-Lagarias Criteria for the Riemann Hypothesis
arXiv: Number Theory, 2020Co-Authors: Lawrence C. Washington, Ambrose YangAbstract:Robin's criterion states that the Riemann Hypothesis is equivalent to $\sigma(n) < e^\gamma n \log\log n$ for all integers $n \geq 5041$, where $\sigma(n)$ is the sum of divisors of $n$ and $\gamma$ is the Euler-Mascheroni constant. We prove that the Riemann Hypothesis is equivalent to the statement that $\sigma(n) < \frac{e^\gamma}{2} n \log\log n$ for all odd numbers $n \geq 3^4 \cdot 5^3 \cdot 7^2 \cdot 11 \cdots 67$. Lagarias's criterion for the Riemann Hypothesis states that the Riemann Hypothesis is equivalent to $\sigma(n) < H_n + \exp{H_n}\log{H_n}$ for all integers $n \geq 1$, where $H_n$ is the $n$th harmonic number. We establish an analogue to Lagarias's criterion for the Riemann Hypothesis by creating a new harmonic series $H^\prime_n = 2H_n - H_{2n}$ and demonstrating that the Riemann Hypothesis is equivalent to $\sigma(n) \leq \frac{3n}{\log{n}} + \exp{H^\prime_n}\log{H^\prime_n}$ for all odd $n \geq 3$. We prove stronger analogues to Robin's inequality for odd squarefree numbers. Furthermore, we find a general formula that studies the effect of the prime factorization of $n$ and its behavior in Robin's inequality.
Matteo Cardella - One of the best experts on this subject based on the ideXlab platform.
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equidistribution rates closed string amplitudes and the Riemann Hypothesis
Journal of High Energy Physics, 2010Co-Authors: Sergio L Cacciatori, Matteo CardellaAbstract:We study asymptotic relations connecting unipotent averages of \( {\text{Sp}}\left( {2g,\mathbb{Z}} \right) \) automorphic forms to their integrals over the moduli space of principally polarized abelian varieties. We obtain reformulations of the Riemann Hypothesis as a class of problems concerning the computation of the equidistribution convergence rate in those asymptotic relations. We discuss applications of our results to closed string amplitudes. Remarkably, the Riemann Hypothesis can be rephrased in terms of ultraviolet relations occurring in perturbative closed string theory.
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equidistribution rates closed string amplitudes and the Riemann Hypothesis
arXiv: High Energy Physics - Theory, 2010Co-Authors: Sergio L Cacciatori, Matteo CardellaAbstract:We study asymptotic relations connecting unipotent averages of $Sp(2g,\mathbb{Z})$ automorphic forms to their integrals over the moduli space of principally polarized abelian varieties. We obtain reformulations of the Riemann Hypothesis as a class of problems concerning the computation of the equidistribution convergence rate in those asymptotic relations. We discuss applications of our results to closed string amplitudes. Remarkably, the Riemann Hypothesis can be rephrased in terms of ultraviolet relations occurring in perturbative closed string theory.
Choe Ryong Gil - One of the best experts on this subject based on the ideXlab platform.
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Riemann Hypothesis and Primorial Number
2014Co-Authors: Choe Ryong GilAbstract:In this paper we consider the Riemann Hypothesis by the primorial numbers. Keywords; Riemann Hypothesis, Primorial number.
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An Equivalent Inequality to the Riemann Hypothesis
2012Co-Authors: Choe Ryong GilAbstract:The Riemann Hypothesis is well known. The Riemann Hypothesis is related with many problems of the analytical number theory. And there have been found some propositions equivalent to one. In particular, the Robin inequality is one of the most famous criterions for the Riemann Hypothesis. In this paper we would show one inequality on the sum of divisors function. This inequality is weaker than the Robin inequality, but equivalent to one.
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The Riemann Hypothesis and the Robin Inequality
2012Co-Authors: Choe Ryong GilAbstract:The Riemann Hypothesis is one of the most important unsolved problems in the modern mathematics. The Riemann Hypothesis is closely related with the distribution of prime numbers. The Robin inequality is one of the famous criterions for the Riemann Hypothesis. The Robin inequality is related with the sum of divisors function. In this paper we prove that the Robin inequality holds unconditionally. The main idea is to prove a certain inequality on the sum of divisors function, whch is equivalent to the Robin
