On mean value formulas for the approximate functional equation of the Riemann zeta-function
β Scribed by I. Kiuchi; N. Yanagisawa
- Publisher
- Springer
- Year
- 2002
- Tongue
- English
- Weight
- 195 KB
- Volume
- 78
- Category
- Article
- ISSN
- 0003-889X
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π SIMILAR VOLUMES
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
For any integer K 2 and positive integer h, we investigate the mean value of |ΞΆ(Ο + it)| 2k Γ log h |ΞΆ(Ο + it)| for all real number 0 < k < K and all Ο > 1 -1/K. In case K = 2, h = 1, this has been studied by Wang in [F.T. Wang, A mean value theorem of the Riemann zeta function, Quart. J. Math. Oxfo