Geodesic
Consecutive Primes in Short Intervals
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and Combinatorial Number Theory, Tome 314 (2021), pp. 152-210.

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

We obtain a lower bound for $\#\{x/2$, $p_{n+m} - p_n\leq y\}$, where $p_n$ is the $n$th prime.
Mots-clés : Euler's totient function
Keywords: sieve methods, distribution of prime numbers. 
@article{TM_2021_314_a8,
     author = {Artyom O. Radomskii},
     title = {Consecutive {Primes} in {Short} {Intervals}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {152--210},
     publisher = {mathdoc},
     volume = {314},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2021_314_a8/}
}
TY  - JOUR
AU  - Artyom O. Radomskii
TI  - Consecutive Primes in Short Intervals
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2021
SP  - 152
EP  - 210
VL  - 314
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2021_314_a8/
LA  - ru
ID  - TM_2021_314_a8
ER  - 
%0 Journal Article
%A Artyom O. Radomskii
%T Consecutive Primes in Short Intervals
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2021
%P 152-210
%V 314
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2021_314_a8/
%G ru
%F TM_2021_314_a8
Artyom O. Radomskii. Consecutive Primes in Short Intervals. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and Combinatorial Number Theory, Tome 314 (2021), pp. 152-210. http://geodesic.mathdoc.fr/item/TM_2021_314_a8/

[1] H. Davenport, Multiplicative Number Theory, Grad. Texts Math., 74, 3rd ed., Springer, New York, 2000 | MR | MR | Zbl

[2] Halberstam H., Richert H.-E., Sieve methods, LMS Monogr., 4, Acad. Press, London, 1974 | MR | Zbl

[3] Hall R.R., Tenenbaum G., Divisors, Cambridge Tracts Math., 90, Cambridge Univ. Press, Cambridge, 1988 | MR | Zbl

[4] A. E. Ingham, The Distribution of Prime Numbers, Cambridge Tracts Math. Math. Phys., 30, Cambridge Univ. Press, London, 1932 | MR

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

[6] K. Prachar, Primzahlverteilung, Grundl. Math. Wiss., 91, Springer, Berlin, 1957 | MR | Zbl

[7] I. M. Vinogradov, Elements of Number Theory, Dover, New York, 1954 | MR | MR | Zbl