Web Page of the Ottawa-Carleton Number Theory Seminar

Year 2017-2018

Abstract: Following ideas of Rubinstein, Sarnak and Fiorilli, we give a general framework for the study of prime number races and Chebyshev’s bias attached to general L-functions L(s) = ∑ _n≥1λ_f(n) n^-s satisfying natural analytic hypotheses. We put the emphasis on weakening the required hypotheses such as GRH or linear independence properties of zeros of L-functions. In particular we establish the existence of the logarithmic density of the set {x ≥ 2 : ∑ _p≤xλ_f(p) ≥ 0} conditionally on a much weaker hypothesis than was previously known. We include applications to new Chebyshev’s bias phenomena that were beyond the reach of the previously known cases.