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On the Zeros of the Riemann Zeta-Function
Journal of the London Mathematical Society, 1999\textit{J. E. Littlewood} proved that the Riemann zeta-function \(\zeta(s)\) always has a zero in the strip \(T\leq \text{Im }s\leq T+c/\log\log\log T\) for \(T\) large enough, where \(c\) is an absolute constant [Proc. Lond. Math. Soc. 22, 234-242 (1924; JFM 50.0229.04)]; \textit{E. C. Titchmarsh} gave a simpler proof [Proc. Camb. Philos. Soc. 28, 273-
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, 2004 The Riemann Zeta Function has a deep connection with the distribution of primes. This expository thesis will explain the techniques used in proving the properties of the Rieman Zeta Function, its analytic continuation to the complex plane, and the ...
Reyes, Ernesto Oscar
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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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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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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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A class of approximations to the Riemann zeta function
Journal of Mathematical Analysis and Applications, 2022Maria Nastasescu, Alexandru Zaharescu
exaly