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Zero-free regions for ζ(s)

Published online by Cambridge University Press:  26 February 2010

C. Ryavec
C. Ryavec
Affiliation:
Department of Mathematics, Santa Clara University, Santa Clara, California
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Extract

Hitherto, little use has been made of the well-known representation

of the Riemann zeta-function, ζ(s), within the critical strip l = {s:s = σ + it, 0 < σ < 1}. Certain variants of (1) have been used to deduce the functional equation of ζ(s), while a simple consequence of (1) itself is that ζ(s) does not vanish on the positive real axis.

Type
Research Article
Information
Mathematika , Volume 22 , Issue 1 , June 1975 , pp. 92 - 96
Copyright
Copyright © University College London 1975

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References

1. Bombieri, E.. “On the Large Sieve”, Mathematika, 12, (1965), 201–225.CrossRefGoogle Scholar
2. Elliott, P. D. T. A.. “On Inequalities of Large Sieve Type”, Acta Arithmetica, 18 (1971), 405–422.Google Scholar
3. Matthews, K. R.. “On an Inequality of Davenport and Halberstam”, J. London Math. Soc., 4 (1972), 638–642.CrossRefGoogle Scholar