Results 131 to 140 of about 82,476 (235)
arXiv, 1999 Through an equivalent condition on the Farey series set forth by Franel and Landau, we prove Riemann Hypothesis for the Riemann zeta-function and the Dirichlet L-function.
arxiv
Partial Sums of the Hurwitz and Allied Functions and Their Special Values
MathematicsWe supplement the formulas for partial sums of the Hurwitz zeta-function and its derivatives, producing more integral representations and generic definitions of important constants.
Nianliang Wang +2 more
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Large gaps between consecutive zeros of the Riemann zeta-function. II [PDF]
arXiv, 2013 Assuming the Riemann Hypothesis we show that there exist infinitely many consecutive zeros of the Riemann zeta-function whose gaps are greater than 2.9 times the average spacing.
arxiv
Some computational formulas related the Riemann zeta-function tails
Journal of Inequalities and Applications, 2016 In this paper we present two computational formulae for one kind of reciprocal sums related to the Riemann zeta-function at integer points s = 4 , 5 $s=4,5$ , which answers an open problem proposed by Lin (J. Inequal. Appl. 2016:32, 2016).
Hongmin Xu
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Sonification of the Riemann Zeta Function [PDF]
Proceedings of the 25th International Conference on Auditory Display (ICAD 2019), 2019 The Riemann zeta function is one of the great wonders of mathematics, with a deep and still not fully solved connection to the prime numbers. It is defined via an infinite sum analogous to Fourier additive synthesis, and can be calculated in various ways.
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arXiv, 2007 The Riemann Hypothesis is a conjecture made in 1859 by the great mathematician Riemann that all the complex zeros of the zeta function $\zeta(s)$ lie on the `critical line' ${Rl} s= 1/2$. Our analysis shows that the assumption of the truth of the Riemann Hypothesis leads to a contradiction.
arxiv
The inverse Riemann zeta function
, 2021 In this article, we develop a formula for an inverse Riemann zeta function such that for $w=ζ(s)$ we have $s=ζ^{-1}(w)$ for real and complex domains $s$ and $w$. The presented work is based on extending the analytical recurrence formulas for trivial and non-trivial zeros as to solve an equation $ζ(s)-w=0$ for a given $w$-domain using logarithmic ...
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Joint universality of the Riemann zeta-function and Lerch zeta-functions
Nonlinear Analysis, 2013 In the paper, we prove a joint universality theorem for the Riemann zeta-function and a collection of Lerch zeta-functions with parameters algebraically independent over the field of rational numbers.
Antanas Laurinčikas +1 more
doaj
Riemann Hypothesis as an Uncertainty Relation [PDF]
arXiv, 2013 Physics is a fertile environment for trying to solve some number theory problems. In particular, several tentative of linking the zeros of the Riemann-zeta function with physical phenomena were reported. In this work, the Riemann operator is introduced and used to transform the Riemann's hypothesis in a Heisenberg-type uncertainty relation, offering a ...
arxiv
A two-dimensional limit discrete theorem for Mellin transforms of the Riemann zeta-function
Lietuvos Matematikos Rinkinys, 2007 In the paper two-dimensional limit theorem for the modified Mellin transform of the Riemann zeta-function is obtained.
Violeta Balinskaitė
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