Goldbach numbers in sparse sequences
Annales de l'Institut Fourier, Volume 48 (1998) no. 2, p. 353-378

We show that for almost all nN, the inequality

|p1+p2- exp (( log n)γ)|<1

has solutions with odd prime numbers p 1 and p 2 , provided 1<γ<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.

Nous montrons que pour presque tout nN, l’inégalité

|p1+p2- exp (( log n)γ)|<1

a des solutions avec p 1 ,p 2 nombres premiers impairs, lorsque 1<γ<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.

     author = {Br\"udern, J\"org and Perelli, Alberto},
     title = {Goldbach numbers in sparse sequences},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {48},
     number = {2},
     year = {1998},
     pages = {353-378},
     doi = {10.5802/aif.1621},
     mrnumber = {99j:11119},
     zbl = {0902.11042},
     language = {en},
     url = {}
Brüdern, Jörg; Perelli, Alberto. Goldbach numbers in sparse sequences. Annales de l'Institut Fourier, Volume 48 (1998) no. 2, pp. 353-378. doi : 10.5802/aif.1621.

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