What can be said about zeros of $\zeta(s)$ sharing the largest real part? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T02:55:47Z http://mathoverflow.net/feeds/question/118534 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/118534/what-can-be-said-about-zeros-of-zetas-sharing-the-largest-real-part What can be said about zeros of $\zeta(s)$ sharing the largest real part? Kevin Smith 2013-01-10T13:43:58Z 2013-01-10T16:21:44Z <p>Specifically, if $\rho$ is such that $\zeta(\rho)=0$ and $\max_{\rho}\Re(\rho)= \Theta$, can anything interesting be said about the number/distribution of zeros on the vertical line $\sigma=\Theta$?</p> <p>Clearly this question is almost as hypothetical as they get, so I welcome conditional answers (though not on RH please), consequences of the Bohr-Landau theorem, consequences of the known behavior of $\zeta(s)$ in the critical strip, etc.</p> <p>Maybe you know something along the lines of If there are finitely/ infinitely many, then...''?</p> <p>I am also interested in why your answer may simply be No.'' </p>