Ergodic Universality Theorems for the Riemann Zeta-Function and other L-Functions
Journal de théorie des nombres de Bordeaux, Volume 25 (2013) no. 2, p. 471-476

We prove a new type of universality theorem for the Riemann zeta-function and other L-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 L (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 = {Steuding, J\"orn},
     title = {Ergodic Universality Theorems for the Riemann Zeta-Function and other $L$-Functions},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {25},
     number = {2},
     year = {2013},
     pages = {471-476},
     doi = {10.5802/jtnb.844},
     mrnumber = {3228316},
     zbl = {1283.11118},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2013__25_2_471_0}
}
Steuding, Jörn. 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. http://www.numdam.org/item/JTNB_2013__25_2_471_0/

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