Discrepancy in modular arithmetic progressions

DOI10.1112/S0010437X22007758MaRDI QIDQ5056330

Jacob Fox, Max Wenqiang Xu, Yunkun Zhou

Publication date: 8 December 2022

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.03929

zbMATH Keywords

Fourier analysisarithmetic progressiondiscrepancycongruencepartial coloring method

Mathematics Subject Classification ID

Congruences; primitive roots; residue systems (11A07) Arithmetic functions; related numbers; inversion formulas (11A25) Ramsey theory (05D10) Arithmetic progressions (11B25) Irregularities of distribution, discrepancy (11K38) Sequences (mod (m)) (11B50) Probabilistic methods in extremal combinatorics, including polynomial methods (combinatorial Nullstellensatz, etc.) (05D40) Arithmetic combinatorics; higher degree uniformity (11B30)

Cites Work

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• Roth's estimate of the discrepancy of integer sequences is nearly sharp
• A panorama of discrepancy theory
• Discrepancy of (centered) arithmetic progressions in \({\mathbb{Z}_p}\)
• The Erdős discrepancy problem
• Constructive Discrepancy Minimization by Walking on the Edges
• Discrepancy in arithmetic progressions
• Remark concerning integer sequences
• Geometric discrepancy. An illustrated guide

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