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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on simple $ a$-points of $ L$-functions


Authors: S. M. Gonek, S. J. Lester and M. B. Milinovich
Journal: Proc. Amer. Math. Soc. 140 (2012), 4097-4103
MSC (2010): Primary 11M06, 11M26
Published electronically: April 10, 2012
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Abstract | References | Similar Articles | Additional Information

Abstract: 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$.


References [Enhancements On Off] (What's this?)

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Additional Information

S. M. Gonek
Affiliation: Department of Mathematics, University of Rochester, Rochester, New York 14627
Email: gonek@math.rochester.edu

S. J. Lester
Affiliation: Department of Mathematics, University of Rochester, Rochester, New York 14627
Email: lester@math.rochester.edu

M. B. Milinovich
Affiliation: Department of Mathematics, University of Mississippi, University, Mississippi 38677
Email: mbmilino@olemiss.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11275-4
PII: S 0002-9939(2012)11275-4
Keywords: $a$-points, simple zeros, Riemann zeta-function, $L$-functions, Selberg class
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
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.