Abstract
Keating and Rudnick studied the variance of the polynomial von Mangoldt function Λ:Fq[t]→C in arithmetic progressions and short intervals using two equidistribution results by Katz. Hall, Keating and Roditty-Gershon then generalised the result for arithmetic progressions for a von Mangoldt function Λρ attached to a Galois representation ρ:Gal(Fq(t)‾/Fq(t))→GLm(Q‾ℓ). We employ a recent equidistribution result by Sawin in order to generalise the corresponding result for short intervals for Λρ.
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