| Title:
|
Upper bounds for the density of universality. II (English) |
| Author:
|
Steuding, Jörn |
| Language:
|
English |
| Journal:
|
Acta Mathematica Universitatis Ostraviensis |
| ISSN:
|
1214-8148 |
| Volume:
|
13 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
73-82 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove explicit upper bounds for the density of universality for Dirichlet series. This complements previous results [15]. Further, we discuss the same topic in the context of discrete universality. As an application we sharpen and generalize an estimate of Reich concerning small values of Dirichlet series on arithmetic progressions in the particular case of the Riemann zeta-function. (English) |
| Keyword:
|
universality |
| Keyword:
|
effectivity |
| Keyword:
|
Riemann zeta-function |
| Keyword:
|
Dirichlet series |
| MSC:
|
11M06 |
| MSC:
|
11M26 |
| MSC:
|
11M41 |
| idZBL:
|
Zbl 1251.11059 |
| idMR:
|
MR2290420 |
| . |
| Date available:
|
2009-12-29T09:17:45Z |
| Last updated:
|
2015-03-15 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137473 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[15] Steuding J.: Upper bounds for the density of universality., Acta Arith. 107 (2003), 195-202 MR 1970823, 10.4064/aa107-2-6 |
| Reference:
|
[16] Steuding J.: Value-distribution of L-functions., Habilitation thesis, Frankfurt 2003, to appear in Lecture Notes of Mathematics, Springer Zbl 1130.11044, MR 2025535 |
| Reference:
|
[17] Titchmarsh E.C.: The theory of the Riemann zeta-function., 2nd ed., revised by D.R. Heath-Brown, Oxford University Press 1986 Zbl 0601.10026, MR 0882550 |
| Reference:
|
[18] Frankenhuijsen M. van: Arithmetic progressions of zeros of the Riemann zeta-function., J. Number Theor. 115 (2005), 360-370 MR 2180508, 10.1016/j.jnt.2005.01.002 |
| Reference:
|
[19] Voronin S.M.: Theorem on the ’universality’ of the Riemann zeta-function., Izv. Akad. Nauk SSSR, Ser. Matem. 39 (1975 (in Russian); engl. translation in Math. USSR Izv. 9 (1975), 443-445 Zbl 0333.30023, MR 0472727 |
| Reference:
|
[20] Voronin S.M.: Analytic properties of Dirichlet generating functions of arithmetic objects., Ph.D. thesis, Moscow, Steklov Math. Institute, 1977 (in Russian) |
| . |
