We prove a new type of universality theorem for the Riemann zeta-function and other -functions (which are universal in the sense of Voronin’s theorem). In contrast to previous universality theorems for the zeta-function or its various generalizations, here the approximating shifts are taken from the orbit of an ergodic transformation on the real line.
Nous prouvons un nouveau type de théorème d’universalité pour la fonction zêta de Riemann et d’autres fonctions (qui sont universelles au sens du théorème de Voronin). Contrairement aux théorèmes d’universalité précédents pour la fonction zêta ou ses généralisations diverses, ici les approximations sont obtenues à partir de l’orbite d’une transformation ergodique sur la droite réelle.
@article{JTNB_2013__25_2_471_0,
author = {J\"orn Steuding},
title = {Ergodic {Universality} {Theorems} for the {Riemann} {Zeta-Function} and other $L${-Functions}},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {471--476},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {25},
number = {2},
year = {2013},
doi = {10.5802/jtnb.844},
mrnumber = {3228316},
zbl = {1283.11118},
language = {en},
url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.844/}
}
TY - JOUR AU - Jörn Steuding TI - Ergodic Universality Theorems for the Riemann Zeta-Function and other $L$-Functions JO - Journal de théorie des nombres de Bordeaux PY - 2013 SP - 471 EP - 476 VL - 25 IS - 2 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.844/ DO - 10.5802/jtnb.844 LA - en ID - JTNB_2013__25_2_471_0 ER -
%0 Journal Article %A Jörn Steuding %T Ergodic Universality Theorems for the Riemann Zeta-Function and other $L$-Functions %J Journal de théorie des nombres de Bordeaux %D 2013 %P 471-476 %V 25 %N 2 %I Société Arithmétique de Bordeaux %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.844/ %R 10.5802/jtnb.844 %G en %F JTNB_2013__25_2_471_0
Jörn Steuding. Ergodic Universality Theorems for the Riemann Zeta-Function and other $L$-Functions. Journal de théorie des nombres de Bordeaux, Volume 25 (2013) no. 2, pp. 471-476. doi : 10.5802/jtnb.844. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.844/
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