Exceptional set estimates in finite fields

2023/02/25 by Bright, Paige, Gan, Shengwen · 4 citations
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2302.13193

Abstract

We study the exceptional set estimate for projections in \mathbbF_qⁿ. For each V∈ G(k,\mathbbFⁿ_q), let π_V: \mathbbF_qⁿ→ V be the projection map. We prove the following result: If A⊂ \mathbbF_qⁿ with #A=q^a (n-1≤ a≤ n) and 0< s<(a+n-2)/(2), then # \V∈ G(n-1,\mathbbFⁿ_q): #π_V(A)lt; q^s \\lessapprox q^n-2. This improves the previous range 0(a+n-2)/(2), then the right hand side above should be at least q^t for some t>n-2.

Cited by

• Bourgain-type projection theorems over finite fields
• Additive structures imply more distances in \mathbbF_q^d
• L^p averages of the discrete Fourier transform and applications
• Restricted projections in positive characteristic via Fourier extension and restriction estimates

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