Results 141 to 150 of about 637 (178)
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Blockchain and the Riemann Zeta Function
2021Proof of Work (PoW) mechanisms used as part of the consensus mechanisms in block chains often have a major drawback namely that resources are only spent on doing the PoW and nothing else. In this paper we propose an adaption of hash based PoW’s. This adaption consists in two aspects, firstly by embedding the space of the hash’s, \(\mathcal{H}\), in the
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2020
As Euler noted, the fact that the series (11.0.1) diverges at \(s=1\) gives another proof that the set of primes is infinite—in fact \(\sum _p(1/p)\) diverges. (This is only the simplest of the connections between properties of the zeta function and properties of primes.)
Richard Beals, Roderick S. C. Wong
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As Euler noted, the fact that the series (11.0.1) diverges at \(s=1\) gives another proof that the set of primes is infinite—in fact \(\sum _p(1/p)\) diverges. (This is only the simplest of the connections between properties of the zeta function and properties of primes.)
Richard Beals, Roderick S. C. Wong
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THEOREM ON THE “UNIVERSALITY” OF THE RIEMANN ZETA-FUNCTION
Mathematics of the USSR-Izvestiya, 1975zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the zeros of the Riemann zeta function
Commentarii mathematici Universitatis Sancti Pauli = Rikkyo Daigaku sugaku zasshi, 2002This paper brings forth estimates of iterated integrals for the classical function \(S(T)\) of analytic number theory, namely \[ S(T) = \tfrac 1\pi\arg\zeta(\tfrac 12+ iT) \] when \(T\) is not equal to any \(\gamma\), where \(\rho = \beta + i\gamma\) denotes generic complex zeros of the Riemann zeta-function \(\zeta(s)\).
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Nature, 1952
The Theory of the Riemann Zeta-Function By Prof. E. C. Titchmarsh. Pp. vii + 346. (Oxford: Clarendon Press; London: Oxford University Press, 1951.) 40s. net.
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The Theory of the Riemann Zeta-Function By Prof. E. C. Titchmarsh. Pp. vii + 346. (Oxford: Clarendon Press; London: Oxford University Press, 1951.) 40s. net.
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2001
Abstract The theory we presented in Chapter 10 works globally over the adeles by simply taking the product of the local theories for p ≥ η .
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Abstract The theory we presented in Chapter 10 works globally over the adeles by simply taking the product of the local theories for p ≥ η .
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A class of approximations to the Riemann zeta function
Journal of Mathematical Analysis and Applications, 2022Maria Nastasescu, Alexandru Zaharescu
exaly
1970
If s is a complex number, with s = σ + it, where σ and t are real, and i2= - 1, the zeta-function of Riemann ζ is defined by the relation $$ \zeta(s)=\sum\limits_{{n =1}}^{\infty}{{n^{{ - s}}}},\quad\sigma >1 $$ (1)
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If s is a complex number, with s = σ + it, where σ and t are real, and i2= - 1, the zeta-function of Riemann ζ is defined by the relation $$ \zeta(s)=\sum\limits_{{n =1}}^{\infty}{{n^{{ - s}}}},\quad\sigma >1 $$ (1)
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