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

Peter Sin; John G. Thompson

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

Number Theory 2010-03-15 v8 Representation Theory

Authors: Peter Sin , John G. Thompson

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 $\Gamma^1(15)$ 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.

Keywords

divisor matrix Dirichlet series SL(2,Z) elliptic curve modular curve Riemann zeta function

Cite

@article{arxiv.0803.1121,
  title  = {The Divisor Matrix, Dirichlet Series and SL(2,Z), II},
  author = {Peter Sin and John G. Thompson},
  journal= {arXiv preprint arXiv:0803.1121},
  year   = {2010}
}

Comments

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. The earlier versions were combined with 0712.0837

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

Abstract

Keywords

Cite

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