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

2008/03/07 by Peter Sin, Sin, Peter, John G. Thompson +1
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #math.NT #math.RT #msc:11M06 #msc:20C12

paper · pdf · doi:10.48550/arxiv.0803.1121

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

arxiv created 2010/03/12 · arxiv updated 2010/03/15

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 Γ¹(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.

Related

• Value at 2 of the L-function of an elliptic curve
• Elliptic gamma functions, triptic curves and SL₃(Z)
• Modular transformations of the elliptic hypergeometric functions, Macdonald polynomials, and the shift operator
• On Divisors of Modular Forms
• Hurwitz - Bernoulli Numbers, Formal Groups and the L - Functions of Elliptic Curves