On polynomials in primes and J. Bourgain's circle method approach to ergodic theorems II
Studia Mathematica, Tome 105 (1993) no. 3, pp. 207-233
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We show that if q is greater than one, T is a measure preserving transformation of the measure space (X,β,μ) and f is in $L^{q}(X,β,μ)$ then if ϕ is a non-constant polynomial mapping the natural numbers to themselves, the averages $π_{N}^{-1} ∑_{1≤p≤N} f(T^{ϕ(p)} x) (N = 1, 2, ...) converge μ almost everywhere. Here p runs over the primes and $π_N$ denotes their number in [1, N].
@article{10_4064_sm_105_3_207_233,
author = {R. Nair},
title = {On polynomials in primes and {J.} {Bourgain's} circle method approach to ergodic theorems {II}},
journal = {Studia Mathematica},
pages = {207--233},
publisher = {mathdoc},
volume = {105},
number = {3},
year = {1993},
doi = {10.4064/sm-105-3-207-233},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-105-3-207-233/}
}
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%0 Journal Article %A R. Nair %T On polynomials in primes and J. Bourgain's circle method approach to ergodic theorems II %J Studia Mathematica %D 1993 %P 207-233 %V 105 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/sm-105-3-207-233/ %R 10.4064/sm-105-3-207-233 %G en %F 10_4064_sm_105_3_207_233
R. Nair. On polynomials in primes and J. Bourgain's circle method approach to ergodic theorems II. Studia Mathematica, Tome 105 (1993) no. 3, pp. 207-233. doi: 10.4064/sm-105-3-207-233
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