Abstract
This paper proves that the real projection of each simple zero of any partial sum of the Riemann zeta function \({\zeta_{n}(s) := \sum_{k=1}^{n} \frac{1}{k^{s}}, n > 2}\) , is an accumulation point of the set {Res : ζ n (s) = 0}.
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Dubon, E., Mora, G., Sepulcre, J.M. et al. A note on the real projection of the zeros of partial sums of Riemann zeta function. RACSAM 108, 317–333 (2014). https://doi.org/10.1007/s13398-012-0094-2
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DOI: https://doi.org/10.1007/s13398-012-0094-2
Keywords
- Zeros of entire functions
- Exponential polynomials
- Almost-periodic functions
- Partial sums of the Riemann zeta function