Polynomial sequences in discrete nilpotent groups of step 2

Alexandru D. Ionescu, Ákos Magyar, Mariusz Mirek, Tomasz Z. Szarek

Research output: Contribution to journalArticlepeer-review


We discuss some of our work on averages along polynomial sequences in nilpotent groups of step 2. Our main results include boundedness of associated maximal functions and singular integrals operators, an almost everywhere pointwise convergence theorem for ergodic averages along polynomial sequences, and a nilpotent Waring theorem. Our proofs are based on analytical tools, such as a nilpotent Weyl inequality, and on complex almost-orthogonality arguments that are designed to replace Fourier transform tools, which are not available in the noncommutative nilpotent setting. In particular, we present what we call a nilpotent circle method that allows us to adapt some of the ideas of the classical circle method to the setting of nilpotent groups.

Original languageEnglish (US)
Article number20230085
JournalAdvanced Nonlinear Studies
Issue number1
StatePublished - Jan 1 2023

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • General Mathematics


  • Weyl inequality
  • discrete nilpotent groups
  • nilpotent circle method
  • pointwise ergodic theorems


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