Abstract:
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 α1,…,αr. For this, linear independence is required over the field of rational numbers for the set {log(m+αj):m∈N0=N∪{0},j=1,…,r}.
Keywords:
Hurwitz zeta-function, linear independence, universality, weak convergence.
The research of the first author is funded by the European Social Fund according to the activity “Improvement of researchers” qualification by implementing world-class R&D projects' of Measure №09.3.3-LMT-K-712-01-0037.
Citation:
A. Laurinčikas, G. Vadeikis, “Joint weighted universality of the Hurwitz zeta-functions”, Algebra i Analiz, 33:3 (2021), 111–128; St. Petersburg Math. J., 33:3 (2022), 511–522
\Bibitem{LauVad21}
\by A.~Laurin{\v{c}}ikas, G.~Vadeikis
\paper Joint weighted universality of the Hurwitz zeta-functions
\jour Algebra i Analiz
\yr 2021
\vol 33
\issue 3
\pages 111--128
\mathnet{http://mi.mathnet.ru/aa1763}
\transl
\jour St. Petersburg Math. J.
\yr 2022
\vol 33
\issue 3
\pages 511--522
\crossref{https://doi.org/10.1090/spmj/1712}
Linking options:
https://www.mathnet.ru/eng/aa1763
https://www.mathnet.ru/eng/aa/v33/i3/p111
This publication is cited in the following 2 articles:
Virginija Garbaliauskienė, Audronė Rimkevičienė, Mindaugas Stoncelis, Darius Šiaučiūnas, “On Value Distribution for the Mellin Transform of the Fourth Power of the Riemann Zeta Function”, Axioms, 14:1 (2025), 34
Audronė Rimkevičienė, Darius Šiaučiūnas, “On Discrete Approximation of Analytic Functions by Shifts of the Lerch Zeta Function”, Mathematics, 10:24 (2022), 4650
Citation in format AMSBIB
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