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

Peter Sin and John G. Thompson
Arxiv ID: 0712.0837Last updated: 1/30/2020
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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