Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. 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
  • $s=1$ line gives: $$\psi(x) = x(1+o(1))$$

  • classical zero free region gives: $$\psi(x) = x + O(x e^{-c \sqrt{\log x}})$$ for some positive constant $\delta$

  • RH gives: $$\psi(x) = x + O(\sqrt{x}\log(x)^2)$$

I hope these are correct,

So I was wondering what error term would we get if someone proved there were no zeros with real part $< 1-\varepsilon$?

and why does Terry Tao say understanding the error term is so important?

share|cite|improve this question
I have seen this type of assumption referred to as a "quasi-Riemann hypothesis". See e.g. p. 5 of (Although it looks weaker, it is not clear that it is any more tractable than RH itself!) – Pete L. Clark Feb 16 '13 at 19:50
up vote 2 down vote accepted

Instead of the exponent $1/2$ as in the $\sqrt x$ in the error, you get the larger $x^{1-\epsilon}$

share|cite|improve this answer

Your Answer


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