A note on simple -points of -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

DOI:
https://doi.org/10.1090/S0002-9939-2012-11275-4

Published electronically:
April 10, 2012

MathSciNet review:
2957199

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove, subject to certain hypotheses, that a positive proportion of the -points of the Riemann zeta-function and Dirichlet -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 -points in fixed strips to the right of the line .

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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:
https://doi.org/10.1090/S0002-9939-2012-11275-4

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.