2
$\begingroup$

Hello,

What is the standard reference (including proofs) for a $\sigma>1-\frac{A}{\log t}$ type zero-free region for the Dedekind zeta-function and also, order estimates for $\zeta_K(s)$ and $\frac{1}{\zeta_K(s)}$ as $t\to\infty$ in such regions?

Thanks.

Improve this question
$\endgroup$
4
  • 1
    $\begingroup$ Have you tried Iwaniec-Kowalski? Chapter 5, if I'm not mistaken. I'm not sure if the proofs are included, but it most certainly is a standard reference. $\endgroup$
    – Peter Humphries
    Commented Oct 29, 2011 at 23:14
  • $\begingroup$ Of course there is no such zero-free region in general, and you'll have to deal with possible Landau-Siegel zeros in general (e.g., for quadratic fields). $\endgroup$
    – Denis Chaperon de Lauzières
    Commented Oct 30, 2011 at 8:53
  • $\begingroup$ (Though I am thinking here of the dependency with respect to the field; there's no problem if it's really the t-aspect, and nothing else, which matters.) $\endgroup$
    – Denis Chaperon de Lauzières
    Commented Oct 30, 2011 at 14:50
  • $\begingroup$ Yes, I just need a region for a fixed field. $\endgroup$
    – kuoytfouy
    Commented Nov 2, 2011 at 0:40

1 Answer 1

Reset to default
4
$\begingroup$

You can find a proof in the paper of Lagarias and Odlyzko on the effective Chebotarev density theorem.

Improve this answer
$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .