# Ergodic Universality Theorems for the Riemann Zeta-Function and other $L$-Functions

Jörn Steuding^{[1]}

- [1] University of Würzburg Emil-Fischer-Str. 40 97074 Würzburg, Germany

Journal de Théorie des Nombres de Bordeaux (2013)

- Volume: 25, Issue: 2, page 471-476
- ISSN: 1246-7405

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topSteuding, Jörn. "Ergodic Universality Theorems for the Riemann Zeta-Function and other $L$-Functions." Journal de Théorie des Nombres de Bordeaux 25.2 (2013): 471-476. <http://eudml.org/doc/275804>.

@article{Steuding2013,

abstract = {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.},

affiliation = {University of Würzburg Emil-Fischer-Str. 40 97074 Würzburg, Germany},

author = {Steuding, Jörn},

journal = {Journal de Théorie des Nombres de Bordeaux},

keywords = {Riemann zeta-function; universality; L-function; jointly unversal family},

language = {eng},

month = {9},

number = {2},

pages = {471-476},

publisher = {Société Arithmétique de Bordeaux},

title = {Ergodic Universality Theorems for the Riemann Zeta-Function and other $L$-Functions},

url = {http://eudml.org/doc/275804},

volume = {25},

year = {2013},

}

TY - JOUR

AU - Steuding, Jörn

TI - Ergodic Universality Theorems for the Riemann Zeta-Function and other $L$-Functions

JO - Journal de Théorie des Nombres de Bordeaux

DA - 2013/9//

PB - Société Arithmétique de Bordeaux

VL - 25

IS - 2

SP - 471

EP - 476

AB - 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.

LA - eng

KW - Riemann zeta-function; universality; L-function; jointly unversal family

UR - http://eudml.org/doc/275804

ER -

## References

top- B. Bagchi, A joint universality theorem for Dirichlet $L$-functions. Math. Z. 181 (1982), 319–334. Zbl0479.10028MR678888
- R. Garunkštis, The effective universality theorem for the Riemann zeta-function, in: ‘Special activity in Analytic Number Theory and Diophantine equations’. Proceedings of a workshop at the Max Planck-Institut Bonn 2002, R.B. Heath-Brown and B. Moroz (eds.), Bonner math. Schriften 360 (2003). Zbl1070.11035MR2075625
- R. Garunkštis, A. Laurinčikas, The Lerch zeta-function. Kluwer Academic Publishers, Dordrecht 2002. Zbl1028.11052MR1979048
- Geon Ho Choe, Computational Ergodic Theory. Springer 2005. Zbl1064.37004MR2130385
- A. Reich, Wertverteilung von Zetafunktionen. Arch. Math. 34 (1980), 440–451. Zbl0431.10025MR593771
- J. Steuding, Value-Distribution of $L$-Functions. Lecture Notes in Mathematics, Vol. 1877, Springer, 2007. Zbl1130.11044MR2330696
- S.M. Voronin, Theorem on the ’universality’ of the Riemann zeta-function. Izv. Akad. Nauk SSSR, Ser. Matem. 39 (1975), 475–486 (in Russian); engl. translation in Math. USSR Izv. 9 (1975), 443–453. Zbl0315.10037MR472727
- S.M. Voronin, On the functional independence of Dirichlet $L$-functions. Acta Arith. 27 (1975), 493–503 (in Russian). Zbl0308.10025MR366836

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