Discrete logarithms in free groups

For the free group on n generators we prove that the discrete logarithm is distributed according to the standard Gaussian when the logarithm is renormalized appropriately.Comment: 9 pages, 1 figure, Corrects a mistake in the Introduction and Section

EVALUATIONS OF A CLASS OF DOUBLE L-VALUES

Abstract. An analytic proof of an evaluation theorem for the “convolution”type double L-values of non-principal characters is given. Along the way, Dirichlet character analogues of generalized single and double polylogarithms are defined. The monodromies of these functions play a pivotal role. 1