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math.NT2018
Weak subconvexity without a Ramanujan hypothesis
Kannan Soundararajan, Jesse Thorner
We describe a new method to obtain weak subconvexity bounds for -functions with mild hypotheses on the size of the Dirichlet coefficients. We verify these hypotheses for all aut…
math.NT2018
A unified and improved Chebotarev density theorem
Jesse Thorner, Asif Zaman
We establish an unconditional effective Chebotarev density theorem that improves uniformly over the well-known result of Lagarias and Odlyzko. As a consequence, we give a new asymp…