Monodromy groups and linearly polymorphic functions

Monodromy Groups and Poincaré Series

Iterated Monodromy Groups

We associate a group IMG(f) to every covering f of a topological space M by its open subset. It is the quotient of the fundamental group π1(M) by the intersection of the kernels of its monodromy action for the iterates fn. Every iterated monodromy group comes together with a naturally defined action on a rooted tree. We present an effective method to compute this action and show how the dynamic...

Twisted L-Functions and Monodromy

Independence of ` of Monodromy Groups

Let X be a smooth curve over a finite field of characteristic p. Let E be a number field, and consider an E-compatible system L = {Lλ} of lisse sheaves on X . This means that for every place λ of E not lying over p, we are given a lisse Eλ-sheaf Lλ on X , and these lisse sheaves are E-compatible with one another in the sense that, for every closed point x of X , the polynomial det(1 − T Frobx,L...

Monodromy of A-hypergeometric functions

Using Mellin-Barnes integrals we give a method to compute a relevant subgroup of the monodromy group of an A-hypergeometric system of differential equations. Presumably this group is the full monodromy group of the system