Matching densities for Galois representations
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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.References
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Additional Information
- Nahid Walji
- Affiliation: Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057, Zürich, Switzerland
- MR Author ID: 898921
- Email: nahid.walji@math.uzh.ch
- 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
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 3309-3316
- MSC (2010): Primary 11F70, 11F80
- DOI: https://doi.org/10.1090/proc/12996
- MathSciNet review: 3503699