Elliott-Halberstam conjecture and the Riemann Hypothesis

  1. 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.
  2. jcsd
  3. 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.
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