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An improved upper bound for the argument of the Riemann zeta-function on the critical line
- Source :
- Mathematics of Computation. 81:1053-1061
- Publication Year :
- 2011
- Publisher :
- American Mathematical Society (AMS), 2011.
-
Abstract
- This paper concerns the function S(T), the argument of the Rie- mann zeta-function along the critical line. The main result is that |S(T)| � 0.111logT + 0.275 log logT + 2.450, which holds for all Te.
- Subjects :
- Algebra and Number Theory
Particular values of Riemann zeta function
Applied Mathematics
Mathematical analysis
Prime-counting function
Riemann zeta function
Combinatorics
Riemann Xi function
Computational Mathematics
Arithmetic zeta function
symbols.namesake
Z function
Riemann hypothesis
symbols
Prime zeta function
Mathematics
Subjects
Details
- ISSN :
- 10886842 and 00255718
- Volume :
- 81
- Database :
- OpenAIRE
- Journal :
- Mathematics of Computation
- Accession number :
- edsair.doi...........038751f820be962a1bcb01aecc60e048
- Full Text :
- https://doi.org/10.1090/s0025-5718-2011-02537-8