Mass formula of division algebras over global function fields

AbstractIn this paper we give two proofs of the mass formula for definite central division algebras over global function fields, due to Denert and Van Geel. The first proof is based on a calculation of Tamagawa measures. The second proof is based on analytic methods, in which we establish the relationship directly between the mass and the value of the associated zeta function at zero

On the Eisenstein ideal over function fields

We study the Eisenstein ideal of Drinfeld modular curves of small levels, and the relation of the Eisenstein ideal to the cuspidal divisor group and the component groups of Jacobians of Drinfeld modular curves. We prove that the characteristic of the function field is an Eisenstein prime number when the level is an arbitrary non square-free ideal of $\mathbb{F}_q[T]$ not equal to a square of a prime.Comment: 42 pages. To appear in J. Number Theory, Special issue in honor of Winnie L