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

Peter Sin; John G. Thompson

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arXiv · 0803.1121

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

Peter Sin·John G. Thompson

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Abstract

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 $Γ^1(15)$ 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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Peter Sin, John G. Thompson. 2010-03-12. The Divisor Matrix, Dirichlet Series and SL(2,Z), II. https://arxiv.org/abs/0803.1121

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