A Factorization of Coefficients for Exponential and Logarithm Series for Function Fields

Let X be an elliptic curve or a ramifying hyperelliptic curve over Fq . We will discuss how to factorize the coefficients of exponential and logarithm series or a Hayes module over such a curve. This allows us to obtain v-adic convergence results for such exponential and logarithm series, for v a “finite” prime. As an application, we can show that the v-adic Goss L-value Lv (1,Psi) is log-algebraic for suitable characters Psi.PhDMathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/170043/1/angusck_1.pd