Geodesic
Estimates of lengths of shortest nonzero vectors in some lattices, II
Diskretnaya Matematika, Tome 33 (2021) no. 2, pp. 117-140.

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

In 1988, Friese et al. put forward lower estimates for the lengths of shortest nonzero vectors for “almost all” lattices of some families in the dimension 3. In 2004, the author of the present paper obtained a similar result for the dimension 4. Here by means of results obtained in part of the paper we show that these estimates also hold in the dimension 5.
Keywords: lattice, shortest nonzero vectors, Minkowski successive minima. 
@article{DM_2021_33_2_a8,
     author = {A. S. Rybakov},
     title = {Estimates of lengths of shortest nonzero vectors in some lattices, {II}},
     journal = {Diskretnaya Matematika},
     pages = {117--140},
     publisher = {mathdoc},
     volume = {33},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2021_33_2_a8/}
}
TY  - JOUR
AU  - A. S. Rybakov
TI  - Estimates of lengths of shortest nonzero vectors in some lattices, II
JO  - Diskretnaya Matematika
PY  - 2021
SP  - 117
EP  - 140
VL  - 33
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2021_33_2_a8/
LA  - ru
ID  - DM_2021_33_2_a8
ER  - 
%0 Journal Article
%A A. S. Rybakov
%T Estimates of lengths of shortest nonzero vectors in some lattices, II
%J Diskretnaya Matematika
%D 2021
%P 117-140
%V 33
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2021_33_2_a8/
%G ru
%F DM_2021_33_2_a8
A. S. Rybakov. Estimates of lengths of shortest nonzero vectors in some lattices, II. Diskretnaya Matematika, Tome 33 (2021) no. 2, pp. 117-140. http://geodesic.mathdoc.fr/item/DM_2021_33_2_a8/

[1] Cassels J.W.S., An Introduction to the Geometry of Numbers, Springer-Verlag, 1959 | MR | MR | Zbl

[2] Prakhar K., Raspredelenie prostykh chisel, Mir, M., 1967, 512 pp.; Prachar K., Primzahlverteilung, Springer-Verlag, Berlin Göttingen Heidelberg, 1957 | MR | Zbl

[3] Rybakov A.S., “The shortest vectors of lattices connected with a linear congruent generator”, Discrete Math. Appl., 14:5 (2004), 479–500 | DOI | MR | Zbl

[4] Rybakov A. S., “Otsenki dlin nenulevykh kratchaishikh vektorov nekotorykh reshetok. I”, Diskretnaya matematika, 33:1 (2021), 31–46 | MR

[5] Feldman N.I., Sedmaya problema Gilberta, Izd-vo MGU, M., 1982, 312 pp.

[6] Friese A.M., Hastad J., Kannan R., Lagarias J.C., Shamir A., “Reconstructing truncated integer variables satisfying linear congruences”, SIAM J. Comput., 17:2 (1988), 262–280 | DOI | MR