LAUSR

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 $$E_n(L,s)$$En(L,s) and prove that this random variable scaled by $$n^{-1}$$n-1 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. Furthermore, we obtain a limit distribution for the frequency of zeros of $$E_n(L,s)$$En(L,s) in vertical strips contained in the half-plane $$\mathfrak {R}s>\frac{n}{2}$$Rs>n2.