We investigate how spectral properties of a measure-preserving system are reflected in the multiple ergodic averages arising from that system. For certain sequences , we provide natural conditions on the spectrum such that, for all , in -norm. In particular, our results apply to infinite arithmetic progressions, , Beatty sequences, , the sequence of squarefree numbers, , and the sequence of prime numbers, . We also obtain a new refinement of Szemerédi's theorem via Furstenberg's correspondence principle.
ASJC Scopus subject areas
- Applied Mathematics