Abstract
AbstractWe prove an upper bound on the density of zeros very close to the critical line of the family of Dirichlet L‐functions of modulus q at height T. To do this, we derive an asymptotic for the twisted second moment of Dirichlet L‐functions uniformly in q and t. As a second application of the asymptotic formula, we prove that, for every integer q, at least 38.2% of zeros of the primitive Dirichlet L‐functions of modulus q lie on the critical line.
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