Elliott-Halberstam conjecture and the Riemann Hypothesis

flouran

I was wondering if one of the consequences of the Elliott-Halberstam conjecture would imply the Riemann Hypothesis (RH) or the Generalized Riemann Hypothesis (GRH)?
Or at least if there is a connection between the Elliott-Halberstam conjecture and RH or GRH?
I ask because the Bombieri-Vinogradov (which is related to the Elliott-Halberstam conjecture) theorem was proven assuming GRH.

kcin94

Neither of EH or GRH is a consequence of the other. As for Bombieri--Vinogradov, while you can prove it from GRH, it is true unconditionally by using Large Sieve techniques.