Variance of sums in short intervals and L-functions in \mathbbF_q[t]

2021/02/12 by Hochfilzer, Leonhard
#11M38 #FOS: Mathematics #Number Theory (math.NT) #primary: 11T55 #secondary: 11M50

paper · doi:10.48550/arxiv.2102.06415

Abstract

Keating and Rudnick studied the variance of the polynomial von Mangoldt function Λ\colon \mathbbF_q[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 Λ_ρ attached to a Galois representation ρ\colon Gal ( \mathbbF_q(t)/\mathbbF_q(t) ) → GL_m(ℚ_ℓ). We employ a recent equidistribution result by Sawin in order to generalise the corresponding result for short intervals for Λ_ρ.

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