Concatenation theorems for anti-Gowers-uniform functions and Host-Kra characteristic factors

Terence Tao, Tamar Ziegler

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


We establish a number of "concatenation theorems" that assert, roughly speaking, that if a function exhibits "polynomial" (or "Gowers anti-uniform", "uniformly almost periodic", or "nilsequence") behaviour in two different directions separately, then it also exhibits the same behavior (but at higher degree) in both directions jointly. Among other things, this allows one to control averaged local Gowers uniformity norms by global Gowers uniformity norms. In a sequel to this paper, we will apply such control to obtain asymptotics for "polynomial progressions" n+P1(r);, n+Pk(r) in various sets of integers, such as the prime numbers.

Original languageAmerican English
Pages (from-to)1-61
Number of pages61
JournalDiscrete Analysis
Issue number2016
StatePublished - 2016

Bibliographical note

Publisher Copyright:
© 2016 Terence Tao and Tamar Ziegler.


  • Concatenation theorems
  • Dual functions
  • Gowers-Host-Kra seminorms


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