On the extreme values of the Riemann zetafunction between its zeros on the critical line

We give new upper bounds (for every theta) of the form

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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.