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arXiv · 2208.07426

A modification of the mixed joint universality theorem for a class of zeta-functions

Benjaminas Togobickij·Roma Kačinskaitė
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Abstract

The property of zeta-functions on mixed joint universality in the Voronin's sense states that any two holomorphic functions can be approximated simultaneously with accuracy $\epsilon>0$ by suitable vertical shifts of the pair consisting from the Riemann zeta- and Hurwitz zeta-functions. In [1], it was shown rather general result, i.e., an approximating pair was composed of the Matsumoto zeta-functions' class and the periodic Hurwitz zeta-function. In this paper, we prove that this set of shifts has a strict positive density for all but at most countably many $\epsilon>0$. Also, we give the concluding remarks on certain more general mixed tuple of zeta-functions.

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Benjaminas Togobickij, Roma Kačinskaitė. 2022-08-15. A modification of the mixed joint universality theorem for a class of zeta-functions. https://doi.org/10.3390/math10193536

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