Quantitative bounds in the inverse theorem for the Gowers U^s+1-norms over cyclic groups

2018/11/02 by Manners, Frederick · 2 citations
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1811.00718

Abstract

We provide a new proof of the inverse theorem for the Gowers U^s+1-norm over groups H=\mathbb Z/N\mathbb Z for N prime. This proof gives reasonable quantitative bounds (the worst parameters are double-exponential), and in particular does not make use of regularity or non-standard analysis, both of which are new for s ≥ 3 in this setting.

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• The Lens of Abelian Embeddings
• Finding arithmetic progressions in dense sets of integers

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