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**1 - 4**of**4**### Multiple recurrence and convergence for certain averages along shifted primes, Available at arXiv:1303.3902

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by N Frantzikinakis, B Host, B Kra

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by
Nikos Frantzikinakis
, 2011

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... polynomials with zero constant term [35], the shifted primes ([191] for powers and [42] in general), integer polynomials with zero constant term evaluated at the shifted primes ([191] for powers and =-=[81]-=- in general), several generalized polynomial sequences [44], and some random sequences of zero density [88]. The sequence ([nc]), where c ∈ R is positive, is known to be good for multiple recurrence o...

by
Wenbo Sun

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... integer coefficients) for a single transformation. After that, these results were generalized to the multi-dimensional polynomial case for commutative transformations by Frantzikinakis, Host and Kra =-=[9]-=-. It is natural to ask whether one can prove a version of these theorems for generalized polynomials. Theorem 1.1 extends these results to linear generalized polynomials. By what is now referred to as...

by
Le, Julia Wolf

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...if we replace p− 1 with p+ 1. 1 2 THÁI HOÀNG LÊ AND JULIA WOLF A generalization to polynomials in several variables, with a simpler proof, was subsequently obtained by Frantzikinakis, Host and Kra =-=[3]-=-. Our goal in this paper is to establish the following hybrid of Theorems 2 and 3. Theorem 4. Let P1, . . . , Pk be polynomials in Z[x] such that Pi(0) = 0 for i = 1, . . . , k. Then any subset of the...

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