• Corpus ID: 119676447

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

@article{Manners2018QuantitativeBI,
title={Quantitative bounds in the inverse theorem for the Gowers \$U^\{s+1\}\$-norms over cyclic groups},
author={Frederick Manners},
journal={arXiv: Combinatorics},
year={2018}
}
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 $s \ge 3$ in this setting.

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