Distribution of Values of L-functions at the Edge of the Critical Strip

Abstract. We prove several results on the distribution of values of L-functions at the edge of the critical strip, by constructing and studying a large class of random Euler products. Among new applications, we provide a precise estimate for the distribution of the values at s = 1 of the family of k-th symmetric power L-functions of primitive cusp forms of weight 2 in the level aspect (assuming the automorphy of these L-functions), using results of Cogdell and Michel on high complex moments of this family. Further we study families of L-functions of the Selberg Class in the t aspect at Re(s) = 1, and of L-functions of quadratic twists of cuspidal automorphic representations of GL(m)/Q at s = 1, and prove precise estimates for the corresponding distribution functions assuming a uniform version of the Sato-Tate conjecture.