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), 40974103
MSC (2010):
Primary 11M06, 11M26
Published electronically:
April 10, 2012
MathSciNet review:
2957199
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Abstract 
References 
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Additional Information
Abstract: We prove, subject to certain hypotheses, that a positive proportion of the points of the Riemann zetafunction 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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 P. J. Bauer, Zeros of Dirichlet series on the critical line, Acta Arith. 93 (2000), 3752. MR 1760087 (2001h:11113)
 2.
 B. C. Berndt, The number of zeros for , J. London Math. Soc. (2) 2 (1970), 577580. MR 0266874 (42:1776)
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 V. Borchsenius and B. Jessen, Mean motions and values of the Riemann zeta function, Acta Math. 80 (1948), 97166. MR 0027796 (10:356b)
 4.
 H. M. Bui, J. B. Conrey, and M. P. Young, More than 41% of the zeros of the zeta function are on the critical line, to appear in Acta Arith. Available on the arXiv at http://arxiv.org/pdf/1002.4127v2.
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 R. Garunkštis and J. Steuding, On the roots of the equation , preprint. Available on the arXiv at http://arxiv.org/abs/1011.5339v1.
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 N. Levinson and H. L. Montgomery, Zeros of the derivatives of the Riemann zetafunction, Acta Math. 133 (1974), 4965. MR 0417074 (54:5135)
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 K. Powell, Topics in analytic number theory, master's thesis, Brigham Young University, Provo, Utah, 2009.
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 A. Selberg, Old and new conjectures and results about a class of Dirichlet series, in: Proceedings of the Amalfi Conference on Analytic Number Theory, Maiori 1989, E. Bombieri et al. (eds.), Università di Salerno, 1992, 367385. MR 1220477 (94f:11085)
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 K. M. Tsang, The distribution of the values of the Riemann zetafunction, Ph.D. dissertation, Princeton Univ., Princeton, NJ, 1984. MR 2633927
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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/S000299392012112754
PII:
S 00029939(2012)112754
Keywords:
$a$points,
simple zeros,
Riemann zetafunction,
$L$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 DMS0653809.
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.
