• Corpus ID: 236881061

Generalized coefficients of the Dirichlet series

@inproceedings{Kapitonets2021GeneralizedCO,
  title={Generalized coefficients of the Dirichlet series},
  author={Kirill Kapitonets},
  year={2021}
}
The paper considers a method for converting a divergent Dirichlet series into a convergent Dirichlet series by directly converting the coefficients of the original series 1→ δn(s) for the Riemann Zeta function. In the first part of the paper, we study the properties of the coefficients δ∗ n of a finite Dirichlet series for approximating the Riemann Zeta function on the interval ∆H . In general, the coefficients δ∗ n of a finite Dirichlet series are complex numbers. The dependence of the… 
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7 References

Approximation of Riemann’s Zeta Function by Finite Dirichlet Series: A Multiprecision Numerical Approach

Finite Dirichlet series are defined by the condition that they vanish at as many initial zeros of the zeta function as possible and can produce extremely good approximations to the values of Riemann’s zetafunction inside the critical strip.

On the zeros of Riemann's zeta-function on the critical line

The Theory of the Riemann Zeta-Function

The Riemann zeta-function embodies both additive and multiplicative structures in a single function, making it our most important tool in the study of prime numbers. This volume studies all aspects…

Divergent Series

Divergent SeriesBy Prof. G. H. Hardy. Pp. xvi + 396. (Oxford: Clarendon Press; London: Oxford University Press, 1949.) 30s. net.

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Oxford At The Clarendon Press

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The Riemann Hypothesis -official problem description (PDF)

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