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Proceedings of the American Mathematical Society

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ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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A note on simple $a$-points of $L$-functions
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by S. M. Gonek, S. J. Lester and M. B. Milinovich PDF
Proc. Amer. Math. Soc. 140 (2012), 4097-4103 Request permission


We prove, subject to certain hypotheses, that a positive proportion of the $a$-points of the Riemann zeta-function and Dirichlet $L$-functions with primitive characters are simple and discuss corresponding results for other functions in the Selberg class. We also prove an unconditional result of this type for the $a$-points in fixed strips to the right of the line $\Re s=1/2$.
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Additional Information
  • S. M. Gonek
  • Affiliation: Department of Mathematics, University of Rochester, Rochester, New York 14627
  • MR Author ID: 198665
  • Email:
  • S. J. Lester
  • Affiliation: Department of Mathematics, University of Rochester, Rochester, New York 14627
  • Email:
  • M. B. Milinovich
  • Affiliation: Department of Mathematics, University of Mississippi, University, Mississippi 38677
  • Email:
  • Received by editor(s): March 18, 2011
  • Received by editor(s) in revised form: May 18, 2011, and May 24, 2011
  • Published electronically: April 10, 2012
  • Additional Notes: Research of the first author was partially supported by NSF grant DMS-0653809.
  • Communicated by: Matthew A. Papanikolas
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 4097-4103
  • MSC (2010): Primary 11M06, 11M26
  • DOI:
  • MathSciNet review: 2957199