Geodesic
On the least almost-prime in arithmetic progression
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 1, pp. 177-188.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Let $\mathcal {P}_r$ denote an almost-prime with at most $r$ prime factors, counted according to multiplicity. Suppose that $a$ and $q$ are positive integers satisfying $(a,q)=1$. Denote by $\mathcal {P}_2(a,q)$ the least almost-prime $\mathcal {P}_2$ which satisfies $\mathcal {P}_2\equiv a\pmod q$. It is proved that for sufficiently large $q$, there holds $$ \mathcal {P}_2(a,q)\ll q^{1.8345}. $$ This result constitutes an improvement upon that of Iwaniec (1982), who obtained the same conclusion, but for the range $1.845$ in place of $1.8345$.
DOI : 10.21136/CMJ.2022.0478-21
Classification : 11N13, 11N35, 11N36
Keywords: almost-prime; arithmetic progression; linear sieve; Selberg's $\Lambda ^2$-sieve 
@article{10_21136_CMJ_2022_0478_21,
     author = {Li, Jinjiang and Zhang, Min and Cai, Yingchun},
     title = {On the least almost-prime in arithmetic progression},
     journal = {Czechoslovak Mathematical Journal},
     pages = {177--188},
     publisher = {mathdoc},
     volume = {73},
     number = {1},
     year = {2023},
     doi = {10.21136/CMJ.2022.0478-21},
     mrnumber = {4541095},
     zbl = {07655761},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2022.0478-21/}
}
TY  - JOUR
AU  - Li, Jinjiang
AU  - Zhang, Min
AU  - Cai, Yingchun
TI  - On the least almost-prime in arithmetic progression
JO  - Czechoslovak Mathematical Journal
PY  - 2023
SP  - 177
EP  - 188
VL  - 73
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2022.0478-21/
DO  - 10.21136/CMJ.2022.0478-21
LA  - en
ID  - 10_21136_CMJ_2022_0478_21
ER  - 
%0 Journal Article
%A Li, Jinjiang
%A Zhang, Min
%A Cai, Yingchun
%T On the least almost-prime in arithmetic progression
%J Czechoslovak Mathematical Journal
%D 2023
%P 177-188
%V 73
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2022.0478-21/
%R 10.21136/CMJ.2022.0478-21
%G en
%F 10_21136_CMJ_2022_0478_21
Li, Jinjiang; Zhang, Min; Cai, Yingchun. On the least almost-prime in arithmetic progression. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 1, pp. 177-188. doi : 10.21136/CMJ.2022.0478-21. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2022.0478-21/

Cité par Sources :