The Divisor Matrix, Dirichlet Series and SL(2,Z)

Details The Divisor Matrix, Dirichlet Series and SL(2,Z) The Divisor Matrix, Dirichlet Series and SL(2,Z)

2007-12-05

arxiv.org/abs/0712.0837v6

Mathematics

Number Theory

29 pages. The current version V4 is the combination of two papers, previously called parts I and II, with the same title. Part

Scientific paper

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.

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