MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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)?

share|cite|improve this question

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

share|cite|improve this answer
Thanks, I'll have a look at it! – 112358 Dec 16 '12 at 4:49

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.