Critical determinant of the region $|x|^p+|y|^p1$ (Supplement to the paper “On the application of the electronic computer to the proof of a conjecture of Minkowski from the geometry of numbers,” Zap. Nauchn. Sem. Lomi, 71, 163–180, 1977)
Zapiski Nauchnykh Seminarov POMI, Studies in number theory. Part 5, Tome 82 (1979), pp. 29-32
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A. V. Malyshev. Critical determinant of the region $|x|^p+|y|^p<1$ (Supplement to the paper “On the application of the electronic computer to the proof of a conjecture of Minkowski from the geometry of numbers,” Zap. Nauchn. Sem. Lomi, 71, 163–180, 1977). Zapiski Nauchnykh Seminarov POMI, Studies in number theory. Part 5, Tome 82 (1979), pp. 29-32. http://geodesic.mathdoc.fr/item/ZNSL_1979_82_a1/
@article{ZNSL_1979_82_a1,
author = {A. V. Malyshev},
title = {Critical determinant of the region $|x|^p+|y|^p<1$ {(Supplement} to the paper {{\textquotedblleft}On} the application of the electronic computer to the proof of a conjecture of {Minkowski} from the geometry of numbers,{\textquotedblright} {Zap.} {Nauchn.} {Sem.} {Lomi,} 71, 163{\textendash}180, 1977)},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {29--32},
year = {1979},
volume = {82},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_82_a1/}
}
TY - JOUR
AU - A. V. Malyshev
TI - Critical determinant of the region $|x|^p+|y|^p<1$ (Supplement to the paper “On the application of the electronic computer to the proof of a conjecture of Minkowski from the geometry of numbers,” Zap. Nauchn. Sem. Lomi, 71, 163–180, 1977)
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1979
SP - 29
EP - 32
VL - 82
UR - http://geodesic.mathdoc.fr/item/ZNSL_1979_82_a1/
LA - ru
ID - ZNSL_1979_82_a1
ER -
%0 Journal Article
%A A. V. Malyshev
%T Critical determinant of the region $|x|^p+|y|^p<1$ (Supplement to the paper “On the application of the electronic computer to the proof of a conjecture of Minkowski from the geometry of numbers,” Zap. Nauchn. Sem. Lomi, 71, 163–180, 1977)
%J Zapiski Nauchnykh Seminarov POMI
%D 1979
%P 29-32
%V 82
%U http://geodesic.mathdoc.fr/item/ZNSL_1979_82_a1/
%G ru
%F ZNSL_1979_82_a1
Supplement to the paper cited in the title. One presents the results of the calculations on an electronic computer, by the method developed in that paper, proving Minkowski's conjecture regarding the critical determinant of the region $|x|^p+|y|^p<1$ for all real numbers $p>2.035$ and for $1.01\leqslant p\leqslant1.99$.
