naa a22 4500 510783295 CHVBK 20180411083254.0 cr unu---uuuuu 180411e20130301xx s 000 0 eng 10.1007/s11856-012-0132-y doi (NATIONALLICENCE)springer-10.1007/s11856-012-0132-y The polynomial multidimensional Szemerédi Theorem along shifted primes [Elektronische Daten] [Nikos Frantzikinakis, Bernard Host, Bryna Kra] If $\vec q_1 ,...,\vec q_m $ : ℤ → ℤ ℓ are polynomials with zero constant terms and E ⊂ ℤ ℓ has positive upper Banach density, then we show that the set E ∩ (E − $\vec q_1 $ (p − 1)) ∩ ... ∩ (E − $\vec q_m $ (p − 1)) is nonempty for some prime p. We also prove mean convergence for the associated averages along the prime numbers, conditional to analogous convergence results along the full integers. This generalizes earlier results of the authors, of Wooley and Ziegler, and of Bergelson, Leibman and Ziegler. Hebrew University Magnes Press, 2012 Frantzikinakis Nikos Department of Mathematics, University of Crete, Knossos Avenue, 71409, Heraklion, Greece aut Host Bernard Laboratoire d'analyse et de mathématiques appliquées, Université de Marne la Vallée & CNRS UMR 8050, 5 Bd. Descartes, Champs sur Marne, 77454, Marne la Vallée Cedex 2, France aut Kra Bryna Department of Mathematics, Northwestern University, 2033 Sheridan Road, 60208-2730, Evanston, IL, USA aut Israel Journal of Mathematics The Hebrew University Magnes Press 194/1(2013-03-01), 331-348 0021-2172 194:1<331 2013 194 11856 https://doi.org/10.1007/s11856-012-0132-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0132-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Frantzikinakis Nikos Department of Mathematics, University of Crete, Knossos Avenue, 71409, Heraklion, Greece aut NATIONALLICENCE 700 1- Host Bernard Laboratoire d'analyse et de mathématiques appliquées, Université de Marne la Vallée & CNRS UMR 8050, 5 Bd. Descartes, Champs sur Marne, 77454, Marne la Vallée Cedex 2, France aut NATIONALLICENCE 700 1- Kra Bryna Department of Mathematics, Northwestern University, 2033 Sheridan Road, 60208-2730, Evanston, IL, USA aut NATIONALLICENCE 773 0- Israel Journal of Mathematics The Hebrew University Magnes Press 194/1(2013-03-01), 331-348 0021-2172 194:1<331 2013 194 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer