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BIT, 1968
Riemanns Zeta-Funktion sei \(\displaystyle P(s) = \sum_{(p)} p^{-s}\), \(s = \sigma + i\tau\), über alle Primzahlen \(p\). Die Schwierigkeiten der Berechnung werden außerordentlich groß in der Nähe der imaginären Achse. Das Haselgrove-Miller-Verfahren, das auf halbkonvergierenden, passend zugestutzten Reihen beruht, findet hier Anwendung.
Carl-Erik Fröberg
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Riemanns Zeta-Funktion sei \(\displaystyle P(s) = \sum_{(p)} p^{-s}\), \(s = \sigma + i\tau\), über alle Primzahlen \(p\). Die Schwierigkeiten der Berechnung werden außerordentlich groß in der Nähe der imaginären Achse. Das Haselgrove-Miller-Verfahren, das auf halbkonvergierenden, passend zugestutzten Reihen beruht, findet hier Anwendung.
Carl-Erik Fröberg
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The Riemann Zeta Function and the Prime Number Theorem
2020For a complex number s, we always denote its real part by \(\sigma \) and imaginary part by t. Thus \(s=\sigma +it.\) The Riemann Zeta function is defined as $$ \zeta (s)=\sum ^{\infty }_{n=1} \ \ \frac{1}{n^s} \ \text {in} \ \sigma > 1.$$
T. Shorey
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Aperiodic crystals, Riemann zeta function, and primes
Structural Chemistry, 2022Alexey E. Madison +2 more
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International Symposium on Symbolic and Algebraic Computation, 2023
Finding roots of a bivariate polynomial f(x1, x2), over a prime field , is a fundamental question with a long history and several practical algorithms are now known.
Sayak Chakrabarti, Nitin Saxena
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Finding roots of a bivariate polynomial f(x1, x2), over a prime field , is a fundamental question with a long history and several practical algorithms are now known.
Sayak Chakrabarti, Nitin Saxena
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, 2023
This article provides a proof of the famous \textit{Prime Number Theorem} by establishing an analogous statement of the same in terms of the second \textit{Chebyshev Function} $\psi(x)$.
Subham De
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This article provides a proof of the famous \textit{Prime Number Theorem} by establishing an analogous statement of the same in terms of the second \textit{Chebyshev Function} $\psi(x)$.
Subham De
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Orbit growth of Dyck and Motzkin shifts via Artin–Mazur zeta function
Dynamical systems, 2020For a discrete dynamical system, the prime orbit and Mertens' orbit counting functions indicate the growth of the closed orbits in the system in a certain way. These functions are analogous to the counting functions for primes in number theory.
Azmeer Nordin +2 more
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The Student Mathematical Library, 2020
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 Riemann zeta function, its analytic continuation to the complex plane, and'the ...
Ernesto Oscar Reyes
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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 Riemann zeta function, its analytic continuation to the complex plane, and'the ...
Ernesto Oscar Reyes
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On primeness of the Selberg zeta-function
2019To appear in Hokkaido Mathematical ...
Garunk��tis, Ram��nas +1 more
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Zeta functions: from prime numbers to K-theory
2022In this thesis, the Riemann zeta function is introduced first through the sieve of Eratosthenes and product formulas, by which its relationship with prime numbers is illustrated. Following this, the analytic continuation of the Riemann zeta function, as well as the Hurwitz zeta function, is discussed from two different perspectives: contour integration
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