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

In: The Legacy of Alladi Ramakrishnan in the Mathematical Sciences

Author

Listed:
  • Peter Sin

    (University of Florida, Department of Mathematics)

  • John G. Thompson

    (University of Florida, Department of Mathematics)

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.

Suggested Citation

  • Peter Sin & John G. Thompson, 2010. "The Divisor Matrix, Dirichlet Series, and SL(2, Z)," Springer Books, in: Krishnaswami Alladi & John R. Klauder & Calyampudi R. Rao (ed.), The Legacy of Alladi Ramakrishnan in the Mathematical Sciences, pages 299-327, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-6263-8_18
    DOI: 10.1007/978-1-4419-6263-8_18
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