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.

29 pages. The current version V4 is the combination of two papers, previously called parts I and II, with the same title. Part II had been posted as arXiv:0803.1121v5. Some additional remarks added in section 10. V6. Minor errors corrected