# Upper bounds for $\zeta(s)$ on the critical line

In Graham and Kolesnik's "Van der Corput's Method of Exponential Sums" they mention the results of Watt (1989) who obtained $\zeta(1/2 + it) = O(t^{89/560 + \epsilon})$.

Is anyone aware of more recent improvements to this bound (and perhaps the methods involved)?

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## 1 Answer

I believe the current record is $O(t^{32/205})$ (where $32/205 \approx .156$) due to Huxley in 2005.

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Thanks, I'll have a look at it! –  112358 Dec 16 '12 at 4:49