How many real zeros does a random Dirichlet series have?
How many real zeros does a random Dirichlet series have?
Let F(σ)= ∑n=1∞Xnnσ be a random Dirichlet series where (Xn)n∈N are independent standard Gaussian random variables. We compute in a quantitative form the expected number of zeros of F(σ) in the interval [T,∞), say EN(T,∞), as T→1∕2+. We also estimate higher moments and with this we derive exponential tails for …