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General $ \Omega$-theorems for coefficients of $ L$-functions


Authors: Jerzy Kaczorowski and Alberto Perelli
Journal: Proc. Amer. Math. Soc. 143 (2015), 5139-5145
MSC (2010): Primary 11N37, 11M41
DOI: https://doi.org/10.1090/proc/12652
Published electronically: June 5, 2015
MathSciNet review: 3411132
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Abstract: We prove a general $ \Omega $-theorem for the coefficients of polynomial combinations of $ L$-functions from the Selberg class. As a consequence, we show that the real and imaginary parts of any linear combination of coefficients of such $ L$-functions have infinitely many sign changes, provided some simple necessary conditions are satisfied.


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Jerzy Kaczorowski
Affiliation: Faculty of Mathematics and Computer Science, A.Mickiewicz University, 61-614 Poznań, Poland — and — Institute of Mathematics of the Polish Academy of Sciences, 00-956 Warsaw, Poland
Email: kjerzy@amu.edu.pl

Alberto Perelli
Affiliation: Dipartimento di Matematica, Università di Genova, via Dodecaneso 35, 16146 Genova, Italy
Email: perelli@dima.unige.it

DOI: https://doi.org/10.1090/proc/12652
Keywords: Sign changes of coefficients, $L$-functions, Selberg class
Received by editor(s): September 4, 2013
Received by editor(s) in revised form: October 11, 2014
Published electronically: June 5, 2015
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2015 American Mathematical Society

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