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Approximating the Riemann Zeta-function by Polynomials with Restricted Zeros

Part of: Miscellaneous topics of analysis in the complex domain Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  17 December 2018

P. M. Gauthier
P. M. Gauthier*
Affiliation:
Département de mathématiques et de statistique, Université de Montréal, CP-6128 Centreville, Montréal, H3C3J7, Canada Email: gauthier@dms.umontreal.ca
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Abstract

We approximate the Riemann Zeta-Function by polynomials and Dirichlet polynomials with restricted zeros.

Keywords

Riemann zeta-functionRiemann Hypothesis

MSC classification

Primary: 30E15: Asymptotic representations in the complex domain
Secondary: 11M26: Nonreal zeros of $zeta (s)$ and $L(s, chi)$; Riemann and other hypotheses
Type
Article
Information
Canadian Mathematical Bulletin , Volume 62 , Issue 3 , September 2019 , pp. 475 - 478
Copyright
© Canadian Mathematical Society 2018 

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Footnotes

Research supported by NSERC (Canada) grant RGPIN-2016-04107.

References

Aron, R. M., Bayart, F., Gauthier, P. M., Maestre, M., and Nestoridis, V., Dirichlet approximation and universal Dirichlet series . Proc. Amer. Math. Soc. 145(2017), no. 10, 4449–4464. https://doi.org/10.1090/proc/13607.Google Scholar
Deutsch, F., Simultaneous interpolation and approximation in topological linear spaces . SIAM J. Appl. Math. 14(1966), 1180–1190. https://doi.org/10.1137/0114095.Google Scholar
Gauthier, P. M., Approximation of and by the Riemann zeta-function . Comput. Methods Funct. Theory 10(2010), no. 2, 603–638. https://doi.org/10.1007/BF03321783.Google Scholar