Geodesic
Joint weighted universality of the Hurwitz zeta-functions
Algebra i analiz, Tome 33 (2021) no. 3, pp. 111-128.

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $\{\log(m+\alpha_j)\colon m\in \mathbb{N}_0=\mathbb{N}\cup\{0\}, j=1,\dots,r\}$.
Keywords: Hurwitz zeta-function, linear independence, universality, weak convergence. 
@article{AA_2021_33_3_a5,
     author = {A. Laurin\v{c}ikas and G. Vadeikis},
     title = {Joint weighted universality of the {Hurwitz} zeta-functions},
     journal = {Algebra i analiz},
     pages = {111--128},
     publisher = {mathdoc},
     volume = {33},
     number = {3},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AA_2021_33_3_a5/}
}
TY  - JOUR
AU  - A. Laurinčikas
AU  - G. Vadeikis
TI  - Joint weighted universality of the Hurwitz zeta-functions
JO  - Algebra i analiz
PY  - 2021
SP  - 111
EP  - 128
VL  - 33
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2021_33_3_a5/
LA  - en
ID  - AA_2021_33_3_a5
ER  - 
%0 Journal Article
%A A. Laurinčikas
%A G. Vadeikis
%T Joint weighted universality of the Hurwitz zeta-functions
%J Algebra i analiz
%D 2021
%P 111-128
%V 33
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2021_33_3_a5/
%G en
%F AA_2021_33_3_a5
A. Laurinčikas; G. Vadeikis. Joint weighted universality of the Hurwitz zeta-functions. Algebra i analiz, Tome 33 (2021) no. 3, pp. 111-128. http://geodesic.mathdoc.fr/item/AA_2021_33_3_a5/

[1] Balčiūnas A., Vadeikis G., “A weighted universality theorem for the Hurwitz zeta-function”, Šiauliai Math. Semin., 12:20 (2017), 5–18

[2] Bagchi B., The statistical behavior and universality properties of the Riemann zeta-function and other allied Dirichlet series, Ph. D. Thesis, Indian Stat. Institute, Calcutta, 1981

[3] Billingsley P., Convergence of probability measures, John Wiley Sons, Inc., 1968 | MR | Zbl

[4] Conway J. B., Functions of one complex variable, Grad. Texts in Math., 11, 2nd ed., Springer-Verlag, New York, 1978 | DOI | MR

[5] Gonek S. M., Analytic properties of zeta and $L$-functions, Ph. D. Thesis, Univ. Michigan, Ann Arbor, 1979 | MR

[6] Laurinčikas A., “The joint universality of Hurwitz zeta-functions”, Šiauliai Math. Semin., 3:11 (2008), 169–187 | MR | Zbl

[7] Laurinčikas A., Garunkštis R., The Lerch zeta-function, Kluwer Acad. Publ., Dordrecht, 2002 | MR | Zbl

[8] Macaitiené R., Stoncelis M., Šiaučiūnas D., “A weighted universality theorem for periodic zeta-functions”, Math. Model. Anal., 22:1 (2017), 95–105 | DOI | MR

[9] Macaitiené R., Stoncelis M., Šiaučiūnas D., “A weighted discrete universality theorem for periodic zeta-functions. II”, Math. Model. Anal., 22:6 (2017), 750–762 | DOI | MR

[10] Mergelyan S. N., “Ravnomernye priblizheniya funktsii kompleksnogo peremennogo”, Uspekhi mat. nauk, 7:2 (1952), 31–122 | MR | Zbl