The divisor matrix, Dirichlet series, and SL(2, Z)

Abstract

A representation of SL(2, Z) by integer matrices acting on the space of analytic ordinary Dirichlet series is constructed, in which the standard unipotent element acts as multiplication by the Riemann zeta function. It is then shown that the Dirichlet series in the orbit of the zeta function are related to it by algebraic equations. © 2010 Springer Science+Business Media, LLC.