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Approximation of and by the Riemann Zeta-Function

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Abstract

It is possible to approximate the Riemann zeta-function by meromorphic functions which satisfy the same functional equation and satisfy (respectively do not satisfy) the analogue of the Riemann hypothesis.

In the other direction, it is possible to approximate meromorphic functions by various manipulations of the Riemann zeta-function.

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  1. Département de mathématiques et de statistique, Université de Montréal, CP-6128, Centreville, Montréal, H3C3J7, Canada

    Paul M. Gauthier

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  1. Paul M. Gauthier
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Correspondence to Paul M. Gauthier.

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Partially supported by TUBITAK (Turkiye) and NSERC (Canada).

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Gauthier, P.M. Approximation of and by the Riemann Zeta-Function. Comput. Methods Funct. Theory 10, 603–638 (2011). https://doi.org/10.1007/BF03321783

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