Joint weighted universality of the Hurwitz zeta-functions. (English) Zbl 1489.11135
St. Petersbg. Math. J. 33, No. 3, 511-522 (2022) and Algebra Anal. 33, No. 3, 111-128 (2021).
Summary: Joint weighted universality theorems are proved concerning simultaneous approximation of a collection of analytic functions by a collection of shifts of Hurwitz zeta-functions with parameters \(\alpha_1,\dots ,\alpha_r\). For this, linear independence is required over the field of rational numbers for the set \(\{\log (m+\alpha_j)\,:\, m\in \mathbb{N}_0=\mathbb{N}\cup \{0\},\;j=1,\dots ,r\} \).
MSC:
| 11M35 | Hurwitz and Lerch zeta functions |
References:
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