Gowers uniformity norms

Target entity: Gowers uniformity norms
Context triple: [Timothy Gowers, notableWork, Gowers uniformity norms]

• A. Szemerédi's theorem
  Szemerédi's theorem is a fundamental result in combinatorial number theory stating that any subset of the integers with positive upper density contains arbitrarily long arithmetic progressions.
• B. Erdős discrepancy problem
  The Erdős discrepancy problem is a famous question in combinatorial number theory that asks whether every infinite ±1 sequence has arbitrarily large discrepancy along some homogeneous arithmetic progression.
• C. Turán–Kubilius inequality
  The Turán–Kubilius inequality is a fundamental result in probabilistic number theory that provides bounds on the distribution of additive arithmetic functions.
• D. Green–Tao theorem
  The Green–Tao theorem is a landmark result in number theory proving that the sequence of prime numbers contains arbitrarily long arithmetic progressions.
• E. Three regularity results in harmonic analysis
  "Three regularity results in harmonic analysis" is the doctoral thesis of mathematician Terence Tao, focusing on advanced problems in harmonic analysis and the study of regularity properties of functions and operators.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Gowers uniformity norms
Target entity description: Gowers uniformity norms are a family of higher-order norms in additive combinatorics used to measure the uniformity of functions and sequences, playing a central role in results such as Szemerédi’s theorem on arithmetic progressions.

• A. Szemerédi's theorem
  Szemerédi's theorem is a fundamental result in combinatorial number theory stating that any subset of the integers with positive upper density contains arbitrarily long arithmetic progressions.
• B. Erdős discrepancy problem
  The Erdős discrepancy problem is a famous question in combinatorial number theory that asks whether every infinite ±1 sequence has arbitrarily large discrepancy along some homogeneous arithmetic progression.
• C. Turán–Kubilius inequality
  The Turán–Kubilius inequality is a fundamental result in probabilistic number theory that provides bounds on the distribution of additive arithmetic functions.
• D. Green–Tao theorem
  The Green–Tao theorem is a landmark result in number theory proving that the sequence of prime numbers contains arbitrarily long arithmetic progressions.
• E. Three regularity results in harmonic analysis
  "Three regularity results in harmonic analysis" is the doctoral thesis of mathematician Terence Tao, focusing on advanced problems in harmonic analysis and the study of regularity properties of functions and operators.
• F. None of above. chosen