We show that for almost all , the inequality
has solutions with odd prime numbers and , provided . 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 , l’inégalité
a des solutions avec nombres premiers impairs, lorsque . 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.
@article{AIF_1998__48_2_353_0, author = {Br\"udern, J\"org and Perelli, Alberto}, title = {Goldbach numbers in sparse sequences}, journal = {Annales de l'Institut Fourier}, pages = {353--378}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {48}, number = {2}, year = {1998}, doi = {10.5802/aif.1621}, zbl = {0902.11042}, mrnumber = {99j:11119}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1621/} }
TY - JOUR AU - Brüdern, Jörg AU - Perelli, Alberto TI - Goldbach numbers in sparse sequences JO - Annales de l'Institut Fourier PY - 1998 SP - 353 EP - 378 VL - 48 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1621/ DO - 10.5802/aif.1621 LA - en ID - AIF_1998__48_2_353_0 ER -
%0 Journal Article %A Brüdern, Jörg %A Perelli, Alberto %T Goldbach numbers in sparse sequences %J Annales de l'Institut Fourier %D 1998 %P 353-378 %V 48 %N 2 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1621/ %R 10.5802/aif.1621 %G en %F AIF_1998__48_2_353_0
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. https://aif.centre-mersenne.org/articles/10.5802/aif.1621/
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