Lethbridge Number Theory and Combinatorics Seminar: Lucile Devin

Following the framework of Rubinstein and Sarnak for Chebyshev's bias, one obtains a limiting logarithmic distribution μ. Then assuming that the zeros of the L-functions are linearly independent over Q, one can show that the distribution μ is smooth.

 

Inspired by the notion of self-sufficient zeros introduced by Martin and Ng, we use a much weaker hypothesis of linear independence to show that the distribution μ is continuous. In particular the existence of one self-sufficient zero is enough to ensure that the bias is well defined.