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Matching densities for Galois representations


Author: Nahid Walji
Journal: Proc. Amer. Math. Soc. 144 (2016), 3309-3316
MSC (2010): Primary 11F70, 11F80
DOI: https://doi.org/10.1090/proc/12996
Published electronically: February 2, 2016
MathSciNet review: 3503699
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Abstract: Given a pair of $ n$-dimensional complex Galois representations over $ \mathbb{Q}$, we define their matching density to be the density, if it exists, of the set of places at which the traces of Frobenius of the two Galois representations are equal. We will show that the set of matching densities of such pairs of irreducible Galois representations (for all $ n$) is dense in the interval $ [0,1]$. We then discuss the automorphic analogue of this problem.


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Additional Information

Nahid Walji
Affiliation: Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057, Zürich, Switzerland
Email: nahid.walji@math.uzh.ch

DOI: https://doi.org/10.1090/proc/12996
Received by editor(s): May 4, 2015
Received by editor(s) in revised form: September 24, 2015, and October 14, 2015
Published electronically: February 2, 2016
Communicated by: Romyar T. Sharifi
Article copyright: © Copyright 2016 American Mathematical Society