Results 211 to 220 of about 82,476 (235)

The Riemann zeta function

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.)
Roderick Wong, Richard Beals
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Riemann’s Zeta Function

2018
The zeta function is defined for ℜ(s) > 1 by $$\displaystyle \zeta (s) = \sum _{n=1}^{+\infty } \frac {1}{n^s}. $$
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On the Riemann zeta-function

Mathematical Proceedings of the Cambridge Philosophical Society, 1932
It was proved by Littlewood that, for every large positive T, ζ (s) has a zero β + iγ satisfyingwhere A is an absolute constant.
E. C. Titchmarsh, G. H. Hardy
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On the extreme values of the Riemann zeta function on random intervals of the critical line

, 2016
In the present paper, we show that under the Riemann hypothesis, and for fixed $$h, \epsilon > 0$$h,ϵ>0, the supremum of the real and the imaginary parts of $$\log \zeta (1/2 + it)$$logζ(1/2+it) for $$t \in [UT -h, UT + h]$$t∈[UT-h,UT+h] are in the ...
J. Najnudel
semanticscholar   +1 more source

THEOREM ON THE “UNIVERSALITY” OF THE RIEMANN ZETA-FUNCTION

, 1975
This paper considers the question of approximating analytic functions by translations of the Riemann zeta-function.Bibliography: 6 items.
S. Voronin
semanticscholar   +1 more source

The Riemann hypothesis and universality of the Riemann zeta-function

Mathematica Slovaca, 2018
We prove that, under the Riemann hypothesis, a wide class of analytic functions can be approximated by shifts ζ(s + iγk), k ∈ ℕ, of the Riemann zeta-function, where γk are imaginary parts of nontrivial zeros of ζ(s).
R. Garunkštis, A. Laurinčikas
semanticscholar   +1 more source

Some Calculations of the Riemann Zeta-Function

, 1953
Introduction IN June 1950 the Manchester University Mark 1 Electronic Computer was used to do some calculations concerned with the distribution of the zeros of the Riemann zeta-function.
A. Turing
semanticscholar   +1 more source

The Riemann Zeta Function

1998
In order to make progress in number theory, it is sometimes necessary to use techniques from other areas of mathematics, such as algebra, analysis or geometry. In this chapter we give some number-theoretic applications of the theory of infinite series.
Gareth Jones, J. Mary Jones
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Riemann Zeta Function

2021
Topic of this chapter is the Riemann zeta function and its non-trivial zeros. The evaluation of the Riemann zeta function is based on a series expansion and if necessary additionally on transforming the function argument. The first 50 non-trivial zeros are table based, additional non-trivial zeros will be numerically evaluated.
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The Riemann zeta function

2010
Number Theory is one of the most ancient and active branches of pure mathematics. It is mainly concerned with the properties of integers and rational numbers. In recent decades, number theoretic methods are also being used in several areas of applied mathematics, such as cryptography and coding theory.
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