A note on simple $a$-points of $L$-functions
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- by S. M. Gonek, S. J. Lester and M. B. Milinovich
- Proc. Amer. Math. Soc. 140 (2012), 4097-4103
- DOI: https://doi.org/10.1090/S0002-9939-2012-11275-4
- Published electronically: April 10, 2012
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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
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Bibliographic Information
- S. M. Gonek
- Affiliation: Department of Mathematics, University of Rochester, Rochester, New York 14627
- MR Author ID: 198665
- 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
- 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: https://doi.org/10.1090/S0002-9939-2012-11275-4
- MathSciNet review: 2957199