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Joint approximation by non-linear shifts of Dirichlet \(L\)-functions. (English) Zbl 1502.11091

Summary: In the paper, a theorem on the simultaneous approximation of a collection of analytic functions by non-linear shifts of Dirichlet \(L\)-functions \((L(s + i t_\tau^{\alpha_1}, \chi_1), \ldots, L(s + i t_\tau^{\alpha_r}, \chi_r))\) is obtained. Here \(t_\tau\) is the Gram function, \(\alpha_1, \ldots, \alpha_r\) are fixed different positive numbers, and \(\chi_1, \ldots, \chi_r\) are arbitrary Dirichlet characters. Also, an example of approximation by a certain composition of the above shifts is given.

MSC:

11M06 \(\zeta (s)\) and \(L(s, \chi)\)
30E10 Approximation in the complex plane
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