Ergodic Universality Theorems for the Riemann Zeta-Function and other -Functions
- [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 -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
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- A. Reich, Wertverteilung von Zetafunktionen. Arch. Math. 34 (1980), 440–451. Zbl0431.10025MR593771
- J. Steuding, Value-Distribution of -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 -functions. Acta Arith. 27 (1975), 493–503 (in Russian). Zbl0308.10025MR366836
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