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On the extreme values of the Riemann zetafunction between its zeros on the critical line
Research output: Contribution to journal › Article › peer-review
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| Journal | Journal für die reine und angewandte Mathematik |
|---|---|
| Date | Published - Jul 2003 |
| Volume | 560 |
| Number of pages | 13 |
| Pages (from-to) | 29-41 |
| Original language | English |
Abstract
We give new upper bounds (for every theta) of the form
[GRAPHICS]
where {t(n)} is the sequence of distinct zeros of \zeta(1/2 + it)\ in R+ and M-n is the maximum between t(n) and t(n+1), k = 1,2. In particular we show that for small theta we have H-k(theta) << theta(3) (with explicit constants): this result might be viewed as unconditional, positive evidence for part of Montgomery's Pair Correlation Conjecture, relating to the small gaps between zeros.
- ZETA-FUNCTION
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