The mean value of the zeta-function on σ=1

The mean value of the zeta-function on σ=1

Let . We derive a precise explicit expression for R ( t ) which is used to derive asymptotic formulas for and . These results improve on earlier upper bounds of Balasubramanian, Ramachandra and the author for the integrals in question.

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Veröffentlicht in:The Ramanujan journal 2011-11, Vol.26 (2), p.209-227
1. Verfasser: Ivić, Aleksandar
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorics
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
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Beschreibung
Zusammenfassung:Let . We derive a precise explicit expression for R ( t ) which is used to derive asymptotic formulas for and . These results improve on earlier upper bounds of Balasubramanian, Ramachandra and the author for the integrals in question.
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-011-9297-y