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

Peter Sin () and John G. Thompson ()
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Peter Sin: University of Florida, Department of Mathematics
John G. Thompson: University of Florida, Department of Mathematics

A chapter in The Legacy of Alladi Ramakrishnan in the Mathematical Sciences, 2010, pp 299-327 from Springer

Abstract: Summary 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.

Keywords: Zeta function; Dirichlet series; Group representation; Divisor matrix (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4419-6263-8_18

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DOI: 10.1007/978-1-4419-6263-8_18

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