On the location of the zero-free half-plane of a random Epstein zeta function
arXiv:1305.1333 · doi:10.1007/s00208-017-1589-0
Abstract
In this note we study, for a random lattice L of large dimension n, the supremum of the real parts of the zeros of the Epstein zeta function E_n(L,s) and prove that this random variable has a limit distribution, which we give explicitly. This limit distribution is studied in some detail; in particular we give an explicit formula for its distribution function.
To appear in Mathematische Annalen. The final publication is available at https://link.springer.com/article/10.1007/s00208-017-1589-0