Mean-Value Theorem of the Riemann Zeta-Function Over Short Intervals

✍ Scribed by A. Sankaranarayanan; K. Srinivas

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 139 KB
• Volume: 45
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.1993.1081

✦ Synopsis

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 small positjve constant, and (T \leqslant l \leqslant T+H) where (H) depends on (T) satisfying (H \leqslant T . \quad 1993) Academic Press. Inc.