The ternary Goldbach problem with a prime and two isolated primes
Informatics and Automation, Analytic and combinatorial number theory, Tome 296 (2017), pp. 192-206.

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove that under the assumption of the Generalized Riemann Hypothesis each sufficiently large odd integer can be expressed as the sum of a prime and two isolated primes.
@article{TRSPY_2017_296_a14,
     author = {H. Maier and M. Rassias},
     title = {The ternary {Goldbach} problem with a prime and two isolated primes},
     journal = {Informatics and Automation},
     pages = {192--206},
     publisher = {mathdoc},
     volume = {296},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2017_296_a14/}
}
TY  - JOUR
AU  - H. Maier
AU  - M. Rassias
TI  - The ternary Goldbach problem with a prime and two isolated primes
JO  - Informatics and Automation
PY  - 2017
SP  - 192
EP  - 206
VL  - 296
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2017_296_a14/
LA  - ru
ID  - TRSPY_2017_296_a14
ER  - 
%0 Journal Article
%A H. Maier
%A M. Rassias
%T The ternary Goldbach problem with a prime and two isolated primes
%J Informatics and Automation
%D 2017
%P 192-206
%V 296
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2017_296_a14/
%G ru
%F TRSPY_2017_296_a14
H. Maier; M. Rassias. The ternary Goldbach problem with a prime and two isolated primes. Informatics and Automation, Analytic and combinatorial number theory, Tome 296 (2017), pp. 192-206. http://geodesic.mathdoc.fr/item/TRSPY_2017_296_a14/

[1] Balog A., Friedlander J., “A hybrid of theorems of Vinogradov and Piatetski-Shapiro”, Pac. J. Math., 156:1 (1992), 45–62 | DOI | MR | Zbl

[2] Balog A., Perelli A., “Exponential sums over primes in an arithmetic progression”, Proc. Amer. Math. Soc., 93 (1985), 587–582 | DOI | MR

[3] de Bruijn N. G., “On the number of positive integers $\leq x$ and free of prime factors $>y$”, Nederl. Acad. Wet. Proc. Ser. A, 54 (1951), 50–60 | MR | Zbl

[4] Erdős P., “On the difference of consecutive primes”, Q. J. Math. Oxford Ser., 6 (1935), 124–128 | MR | Zbl

[5] Erdős P., Nathanson M. B., “Lagrange's theorem and thin subsequences of squares”, Contributions to probability, eds. J. Gani, V. K. Rohatgi, Acad. Press, New York, 1981, 3–9 | MR

[6] Ford K., Green B., Konyagin S., Maynard J., Tao T., Long gaps between primes, E-print, 2014, arXiv: 1412.5029v2[math.NT]

[7] Ford K., Green B., Konyagin S., Tao T., “Large gaps between consecutive prime numbers”, Ann. Math. Ser. 2, 183:3 (2016), 935–974 ; arXiv: 1408.4505[math.NT] | DOI | MR | Zbl

[8] Halberstam H., Richert H.-E., Sieve methods, Acad. Press, London, 1974 | MR | Zbl

[9] Helfgott H. A., Major arcs for Goldbach's theorem, E-print, 2013, arXiv: 1305.2897v1[math.NT]

[10] Helfgott H. A., Platt D. J., “Numerical verification of the ternary Goldbach conjecture up to $8875\cdot10^{30}$”, Exp. Math., 22:4 (2013), 406–409 | DOI | MR | Zbl

[11] Iwaniec H., Lectures on the Riemann zeta function, Univ. Lect. Ser., 62, Amer. Math. Soc., Providence, RI, 2014 | DOI | MR | Zbl

[12] Iwaniec H., Kowalski E., Analytic number theory, AMS Colloq. Publ., 53, Amer. Math. Soc., Providence, RI, 2004 | MR | Zbl

[13] Liu J., Zhan T., “The ternary Goldbach problem in arithmetic progressions”, Acta arith., 82:3 (1997), 197–227 | MR | Zbl

[14] Maier H., Pomerance C., “Unusually large gaps between consecutive primes”, Trans. Amer. Math. Soc., 322:1 (1990), 201–237 | DOI | MR | Zbl

[15] Maynard J., “Large gaps between primes”, Ann. Math. Ser. 2, 183:3 (2016), 915–933 ; arXiv: 1408.5110[math.NT] | DOI | MR | Zbl

[16] Pyatetskii-Shapiro I. I., “O raspredelenii prostykh chisel v posledovatelnostyakh vida $[f(n)]$”, Mat. sb., 33(75):3 (1953), 559–566 | MR | Zbl

[17] Pintz J., “Very large gaps between consecutive primes”, J. Number Theory, 63:2 (1997), 286–301 | DOI | MR | Zbl

[18] Rademacher H., “Über eine Erweiterung des Goldbachschen Problems”, Math. Z., 25 (1926), 627–657 | DOI | MR | Zbl

[19] Rankin R. A., “The difference between consecutive prime numbers”, J. London Math. Soc., 13 (1938), 242–247 | DOI | MR | Zbl

[20] Rankin R. A., “The difference between consecutive prime numbers. V”, Proc. Edinburgh Math. Soc. Ser. 2, 13 (1963), 331–332 | DOI | MR | Zbl

[21] Rassias M. Th., Goldbach's conjecture, Selected topics, Springer, New York (to appear)

[22] Schönhage A., “Eine Bemerkung zur Konstruktion großer Primzahllücken”, Arch. Math., 14 (1963), 29–30 | DOI | MR | Zbl

[23] Vinogradov I. M., “Predstavlenie nechetnogo chisla summoi trekh prostykh chisel”, DAN SSSR, 15:6–7 (1937), 291–294

[24] Westzynthius E., “Über die Verteilung der Zahlen, die zu den $n$ ersten Primzahlen teilerfremd sind”, Commentat. Phys.-Math. Helsingfors, 5:25 (1931), 1–37 | Zbl

[25] Wirsing E., “Thin subbases”, Analysis, 6 (1986), 285–308 | DOI | MR | Zbl