Geodesic
Discrete universality in the Selberg class
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic number theory, Tome 299 (2017), pp. 155-169

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

The Selberg class $\mathcal S$ consists of functions $L(s)$ that are defined by Dirichlet series and satisfy four axioms (Ramanujan conjecture, analytic continuation, functional equation, and Euler product). It has been known that functions in $\mathcal S$ that satisfy the mean value condition on primes are universal in the sense of Voronin, i.e., every function in a sufficiently wide class of analytic functions can be approximated by the shifts $L(s+i\tau )$, $\tau \in \mathbb R$. In this paper we show that every function in the same class of analytic functions can be approximated by the discrete shifts $L(s+ikh)$, $k=0,1,\dots $, where $h>0$ is an arbitrary fixed number.
Keywords: Selberg class, limit theorem, weak convergence, universality. 
@article{TM_2017_299_a9,
     author = {A. Laurin\v{c}ikas and R. Macaitien\.{e}},
     title = {Discrete universality in the {Selberg} class},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {155--169},
     publisher = {mathdoc},
     volume = {299},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2017_299_a9/}
}
TY  - JOUR
AU  - A. Laurinčikas
AU  - R. Macaitienė
TI  - Discrete universality in the Selberg class
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2017
SP  - 155
EP  - 169
VL  - 299
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2017_299_a9/
LA  - ru
ID  - TM_2017_299_a9
ER  - 
%0 Journal Article
%A A. Laurinčikas
%A R. Macaitienė
%T Discrete universality in the Selberg class
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2017
%P 155-169
%V 299
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2017_299_a9/
%G ru
%F TM_2017_299_a9
A. Laurinčikas; R. Macaitienė. Discrete universality in the Selberg class. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic number theory, Tome 299 (2017), pp. 155-169. http://geodesic.mathdoc.fr/item/TM_2017_299_a9/