Joint discrete universality of Hurwitz zeta functions

A. Laurinčikas

Sbornik. Mathematics, Tome 205 (2014) no. 11, pp. 1599-1619

Résumé

We obtain a joint discrete universality theorem for Hurwitz zeta functions. Here the parameters of zeta functions and the step of shifts of these functions approximating a given family of analytic functions are connected by some condition of linear independence. Nesterenko's theorem gives an example satisfying this condition. The universality theorem is applied to estimate the number of zeros of a linear combination of Hurwitz zeta functions. Bibliography: 20 titles.

Détail

Keywords: algebraic independence, Hurwitz zeta function, linear independence, limit theorem, space of analytic functions, joint universality.

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