Two random constructions inside lacunary sets
Annales de l'Institut Fourier, Tome 49 (1999) no. 6, pp. 1853-1867.

Nous étudions le rapport entre la croissance d’une suite d’entiers et les propriétés harmoniques et fonctionnelles de la suite de caractères associée. Nous montrons en particulier que toute suite polynomiale, ainsi que la suite des nombres premiers, contient un ensemble Λ(p) pour tout p qui n’est pas de Rosenthal.

We study the relationship between the growth rate of an integer sequence and harmonic and functional properties of the corresponding sequence of characters. In particular we show that every polynomial sequence contains a set that is Λ(p) for all p but is not a Rosenthal set. This holds also for the sequence of primes.

@article{AIF_1999__49_6_1853_0,
     author = {Neuwirth, Stefan},
     title = {Two random constructions inside lacunary sets},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {49},
     number = {6},
     year = {1999},
     pages = {1853-1867},
     doi = {10.5802/aif.1740},
     mrnumber = {2001c:42007},
     zbl = {0955.42009},
     language = {en},
     url = {aif.centre-mersenne.org/item/AIF_1999__49_6_1853_0/}
}
Neuwirth, Stefan. Two random constructions inside lacunary sets. Annales de l'Institut Fourier, Tome 49 (1999) no. 6, pp. 1853-1867. doi : 10.5802/aif.1740. https://aif.centre-mersenne.org/item/AIF_1999__49_6_1853_0/

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