turkmath.org

After a brief introduction on the value-distribution of arithmetic functions and L-functions, we give an overview of our joint work with Alia Hamieh (University of Northern British Colombia) on the value-distribution of logarithmic derivative of certain automorphic L-functions. Among other things, we describe an upper bound for the discrepancy of the distribution of the values (at a point on the edge of the critical strip) of the twists of a fixed automorphic L-function with quadratic Dirichlet characters. Our result can be considered as an automorphic analogue of a result of Lamzouri, Lester, and Radziwill for the logarithm of the Riemann zeta function. Our estimate is conditional on certain expected bounds on the local parameters of L-functions which is known to be true for GL(1) and GL(2).