Geodesic
On Statistical Properties of Local Minima of Integer Lattices
Dalʹnevostočnyj matematičeskij žurnal, Tome 12 (2012) no. 2, pp. 201-230.

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

The asymptotical formula for average number of local minima of integer multidimensional lattices is proved. 
@article{DVMG_2012_12_2_a7,
     author = {A. A. Illarionov},
     title = {On {Statistical} {Properties} of {Local} {Minima} of {Integer} {Lattices}},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {201--230},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2012_12_2_a7/}
}
TY  - JOUR
AU  - A. A. Illarionov
TI  - On Statistical Properties of Local Minima of Integer Lattices
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2012
SP  - 201
EP  - 230
VL  - 12
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2012_12_2_a7/
LA  - ru
ID  - DVMG_2012_12_2_a7
ER  - 
%0 Journal Article
%A A. A. Illarionov
%T On Statistical Properties of Local Minima of Integer Lattices
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2012
%P 201-230
%V 12
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2012_12_2_a7/
%G ru
%F DVMG_2012_12_2_a7
A. A. Illarionov. On Statistical Properties of Local Minima of Integer Lattices. Dalʹnevostočnyj matematičeskij žurnal, Tome 12 (2012) no. 2, pp. 201-230. http://geodesic.mathdoc.fr/item/DVMG_2012_12_2_a7/

[1] P. M. Gruber, K. G. Lekkerkerker, Geometriya chisel, Nauka, M., 2008, 727 pp. | Zbl

[2] G. F. Voronoi, Sobranie sochinenii v 3-kh tomakh, v. 1, Izd-vo AN USSR, Kiev, 1952

[3] H. Minkowski, “Generalisation de la theorie des fraction continues”, Ann. Sci. Ècole Norm. Sup., 13:2 (1896), 41–60 | MR | Zbl

[4] A. J. Brentjes, Multidimensional continued fraction algorithms, Mathematical Centre Tracts, 145, Mathematisch Centrum, Amsterdam, 1981, 183 pp. | MR

[5] J. Buchmann, M. Pohst, J. v. Schmettow, “On the computation of unit group and class groups of totally real quartic fields”, Math. Comp., 53:187 (1989), 387–397 | DOI | MR | Zbl

[6] V. A. Bykovskii, “O pogreshnosti teoretiko-chislovykh kvadraturnykh formul”, Chebyshevskii sb., 3:2 (2002), 27–33, Tula | MR | Zbl

[7] V. A. Bykovskii, “O pogreshnosti teoretiko-chislovykh kvadraturnykh formul”, DAN, 382:2 (2003), 154–155 | MR

[8] V. A. Bykovskii, “Otkloneniya setok Korobova”, Izv. RAN. Ser. matem., 76:3 (2012), 19–38 | DOI | MR | Zbl

[9] A. A. Illarionov, “O tsilindricheskikh minimumakh trekhmernykh reshetok”, Dalnevost. matem. zhurn., 11:1 (2011), 37–47 | MR | Zbl

[10] A. A. Illarionov, “O tsilindricheskikh minimumakh tselochislennykh reshetok”, Algebra i analiz, 24:2 (2012), 154–170 | MR

[11] A. A. Illarionov, “Srednee kolichestvo otnositelnykh minimumov trekhmernykh tselochislennykh reshetok”, Algebra i analiz, 23:3 (2011), 189–215 | MR

[12] A. A. Illarionov, “On the Asymptotic Distribution of Integer Matrices”, Moscow Journal of Combinatorics and Number Theory, 1:4 (2011), 301–345 | MR

[13] Dzh. V. Kassels, Vvedenie v geometriyu chisel, Mir, M., 1995