A generalized converse measurability theorem

A Converse to Dye’s Theorem

Every non-amenable countable group induces orbit inequivalent ergodic equivalence relations on standard Borel probability spaces. Not every free, ergodic, measure preserving action of F2 on a standard Borel probability space is orbit equivalent to an action of a countable group on an inverse limit of finite spaces. There is a treeable non-hyperfinite Borel equivalence relation which is not univ...

Weil Converse Theorem

Hecke generalized this equivalence, showing that an integral form has an associated Dirichlet series which can be analytically continued to C and satisfies a functional equation. Conversely, Weil showed that, if a Dirichlet series satisfies certain functional equations, then it must be associated to some integral form. Our goal in this paper is to describe this work. In the first three sections...

Generalized Silver and Miller measurability

1 We present some results about the burgeoning research area concerning set theory of the “κ-reals”. We focus on some notions of measurability coming from generalizations of Silver and Miller trees. We present analogies and mostly differences from the classical setting.

Ribet’s Converse to Herbrand’s Theorem

Weil’s converse theorem with poles

We prove a generalization of the classical converse theorem of Weil, allowing the twists by non-trivial Dirichlet characters to have arbitrary poles.