𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The mean value of the zeta-function onσ=1

✍ Scribed by Aleksandar Ivić

Publisher
Springer US
Year
2011
Tongue
English
Weight
607 KB
Volume
26
Category
Article
ISSN
1382-4090

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

Mean-Value Theorem of the Riemann Zeta-F
Mean-Value Theorem of the Riemann Zeta-Function Over Short Intervals
✍ A. Sankaranarayanan; K. Srinivas 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 139 KB

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

A logarithm type mean value theorem of t
A logarithm type mean value theorem of the Riemann zeta function
✍ Xia-Qi Ding; Shao-Ji Feng 📂 Article 📅 2006 🏛 Elsevier Science 🌐 English ⚖ 90 KB

For any integer K 2 and positive integer h, we investigate the mean value of |ζ(σ + it)| 2k × log h |ζ(σ + it)| for all real number 0 < k < K and all σ > 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