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

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

2008-03-07

arxiv.org/abs/0803.1121v8

Mathematics

Number Theory

11 pages.v8 is a minor revison of v7. The paper (v7 on) has different content from the earlier paper (v1-5) of the same title.

Scientific paper

We examine an elliptic curve constructed in an earlier paper from a certain representation of $\SL(2,\Z)$ on the space of convergent Dirichlet series. The curve is observed to be a modular curve for $\Gamma^1(15)$ and a certain orbit of modular functions is thereby associated with the Riemann zeta function. Explicit descriptions are given of these functions and of the permutation action of $\SL(2,\Z)$ on them.

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