Goldbach numbers in sparse sequences

Brüdern, Jörg; Perelli, Alberto

Brüdern, Jörg ; Perelli, Alberto

Annales de l'Institut Fourier, Tome 48 (1998), p. 353-378 / Harvested from Numdam

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Résumé
Abstract

Nous montrons que pour presque tout $n \in N$ , l’inégalité

| p_{1} + p_{2} - \exp ((\log n)^{γ}) | < 1

a des solutions avec $p_{1}, p_{2}$ nombres premiers impairs, lorsque $1 < γ < \frac{3}{2}$ . De plus, nous améliorons la borne de l’ensemble exceptionnel.

Ce résultat fournit presque tous les résultats sur les nombres de Goldbach dans des suites un peu plus fines que les valeurs prises par un polynôme.

We show that for almost all $n \in N$ , the inequality

| p_{1} + p_{2} - \exp ((\log n)^{γ}) | < 1

has solutions with odd prime numbers $p_{1}$ and $p_{2}$ , provided $1 < γ < \frac{3}{2}$ . Moreover, we give a rather sharp bound for the exceptional set.

This result provides almost-all results for Goldbach numbers in sequences rather thinner than the values taken by any polynomial.

Publié le : 1998-01-01

MR 99j:11119 | Zbl 0902.11042

DOI : https://doi.org/10.5802/aif.1621

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     author = {Br\"udern, J\"org and Perelli, Alberto},
     title = {Goldbach numbers in sparse sequences},
     journal = {Annales de l'Institut Fourier},
     volume = {48},
     year = {1998},
     pages = {353-378},
     doi = {10.5802/aif.1621},
     mrnumber = {99j:11119},
     zbl = {0902.11042},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1998__48_2_353_0}
}

Brüdern, Jörg; Perelli, Alberto. Goldbach numbers in sparse sequences. Annales de l'Institut Fourier, Tome 48 (1998) pp. 353-378. doi : 10.5802/aif.1621. http://gdmltest.u-ga.fr/item/AIF_1998__48_2_353_0/

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