Approximating Euler products and class number computation in algebraic function fields
Renate Scheidler, Andreas Stein · Rocky Mountain Journal of Mathematics · 2010
Abstract. We provide a number of results that can be used to derive approximations for the Euler product representation of the zeta function of an arbitrary algebraic function field. Three such approximations are given here. Our results have two main applications. They lead to a computationally suitable algorithm for computing the class number of an arbitrary function field. The ideas underlying the class number algorithms in turn can be used to analyze the distribution of the zeros of its zeta function. 1.