A nilpotent Roth theorem.
From MaRDI portal
Publication:1608555
DOI10.1007/s002220100179zbMath1042.37001OpenAlexW2090562664MaRDI QIDQ1608555
Vitaly Bergelson, Alexander Leibman
Publication date: 8 August 2002
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s002220100179
Measure-preserving transformations (28D05) Dynamical aspects of measure-preserving transformations (37A05) Ergodicity, mixing, rates of mixing (37A25) Weyl sums (11L15) General groups of measure-preserving transformations and dynamical systems (37A15)
Related Items
Discrete Radon transforms and applications to ergodic theory ⋮ Some open problems on multiple ergodic averages ⋮ On the multiple recurrence properties for disjoint systems ⋮ Norm convergence of continuous-time polynomial multiple ergodic averages ⋮ Multiple ergodic averages for variable polynomials ⋮ Pointwise convergence of certain continuous-time double ergodic averages ⋮ Pointwise ergodic theorems for non-conventional bilinear polynomial averages ⋮ On a multi-parameter variant of the Bellow–Furstenberg problem ⋮ Polynomial sequences in discrete nilpotent groups of step 2 ⋮ Joint ergodicity of piecewise monotone interval maps ⋮ Polynomial ergodic averages of measure-preserving systems acted by \(\mathbb{Z}^d\) ⋮ Pointwise multiple averages for sublinear functions ⋮ Multiple recurrence and convergence without commutativity ⋮ Polynomial averages and pointwise ergodic theorems on nilpotent groups ⋮ Oscillation inequalities in ergodic theory and analysis: one-parameter and multi-parameter perspectives ⋮ Norm convergence of nilpotent ergodic averages ⋮ Analysis and applications: The mathematical work of Elias Stein ⋮ On the norm convergence of non-conventional ergodic averages ⋮ Norm convergence of multiple ergodic averages on amenable groups ⋮ Maximal operators associated to discrete subgroups of nilpotent Lie groups ⋮ Sequences from zero entropy noncommutative toral automorphisms and Sarnak conjecture ⋮ A non-singular dynamical system without maximal ergodic inequality ⋮ Probabilistic nilpotence in infinite groups ⋮ Poincaré recurrence and number theory: thirty years later ⋮ A selection of open problems ⋮ Polynomial mappings of groups ⋮ Equidistribution of joinings under off-diagonal polynomial flows of nilpotent Lie groups ⋮ Pleasant extensions retaining algebraic structure. II