Matching densities for Galois representations

Walji, Nahid

doi:10.1090/proc/12996

Matching densities for Galois representations
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Proc. Amer. Math. Soc. 144 (2016), 3309-3316 Request permission

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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