Geodesic
Primes in tuples and Romanoff's theorem
Izvestiya. Mathematics , Tome 89 (2025) no. 1, pp. 125-139.

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

A lower bound for the number of primes in tuples is obtained. As an application, a lower bound for the Romanoff type representation functions is given.
Keywords: prime number, Bombieri–Vinogradov type theorem, representation function, Romanoff's theorem.
Mots-clés : primes in tuples 
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A. O. Radomskii. Primes in tuples and Romanoff's theorem. Izvestiya. Mathematics , Tome 89 (2025) no. 1, pp. 125-139. http://geodesic.mathdoc.fr/item/IM2_2025_89_1_a5/

[1] Yitang Zhang, “Bounded gaps between primes”, Ann. of Math. (2), 179:3 (2014), 1121–1174 | DOI | MR | Zbl

[2] J. Maynard, “Small gaps between primes”, Ann. of Math. (2), 181:1 (2015), 383–413 | DOI | MR | Zbl

[3] J. Maynard, “Dense clusters of primes in subsets”, Compos. Math., 152:7 (2016), 1517–1554 | DOI | MR | Zbl

[4] Yong-Gao Chen and Yuchen Ding, “Quantitative results of the Romanov type representation functions”, Q. J. Math., 74:4 (2023), 1331–1359 | DOI | MR | Zbl

[5] N. P. Romanoff, “Über einige Sätze der additiven Zahlentheorie”, Math. Ann., 109:1 (1934), 668–678 | DOI | MR | Zbl

[6] P. Erdős, “On integers of the form $2^k+p$ and some related problems”, Summa Brasil. Math., 2 (1950), 113–123 | MR | Zbl

[7] Yong-Gao Chen and Yuchen Ding, “On a conjecture of Erdős”, C. R. Math. Acad. Sci. Paris, 360 (2022), 971–974 | DOI | MR | Zbl

[8] H. Davenport, Multiplicative number theory, Grad. Texts in Math., 74, 3rd ed., Springer-Verlag, New York, 2000 | MR | Zbl

[9] M. Ram Murty, Problems in analytic number theory, Grad. Texts in Math., 206, Read. Math., 2nd ed., Springer, New York, 2008 | DOI | MR | Zbl

[10] A. O. Radomskii, “Consecutive primes in short intervals”, Proc. Steklov Inst. Math., 314 (2021), 144–202 | DOI