arXiv subjects

John G. Thompson

Publications and source records attributed to John G. Thompson.

2 recordsLinked to original sources

arXiv2010

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

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.

math.NT↗

arXiv2008

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

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.

math.NT↗