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On the divisor function and the Riemann zeta-function in short intervals

✍ Scribed by Aleksandar Ivić


Publisher
Springer US
Year
2008
Tongue
English
Weight
371 KB
Volume
19
Category
Article
ISSN
1382-4090

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Let \(s=\sigma+i t\). Then, on the assumption of Riemann Hypothesis, we prove the Mean-Value Theorem for the square of the Riemann zeta-function over shorter intervals for \(1 / 2+A_{1} / \log \log T \leqslant \sigma \leqslant 1-\delta\). Here \(A_{1}\) is a large positive constant, \(\delta\) is a

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In this paper, we continue the investigation of the zeta function of divisors, as introduced by the first author in Wan (in: D. Jungnickel, H. Niederreiter (Eds.), Finite Fields and Applications, Springer, Berlin, 2001, pp. 437-461; Manuscripta Math. 74 (1992) 413), for a projective variety over a f