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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, Number 10, Pages 92–97 (Mi ivm9170)  
Brief communications

“Geometry of numbers” in a context of algebraic theory of numbers

Zh. N. Temirgaliyevaa, N. Temirgaliyevb

a University of Southern California, Los Angeles, CA, USA
b Institute of Theoretical Mathematics and Scientific Computing, L. N. Gumilyov Eurasian National University, 2 Satpayev str., Astana, 010008 Republic of Kazakhstan
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Abstract: As noted in circumstantial monograph Geometry of Numbers by P. M. Gruber and C. G. Lekkerkerker, lately there is no considerable contribution to classical theory of calculation and estimates of critical determinants. In this article, in a certain sense, we fill a gap in occurred retardation in developing this theme. We propose a new theoretical-numerical approach with numerous consequences which, in fact, allows to revise all these subjects from another position.
Keywords: geometry of numbers, divisors theory, Euler–Fermat theorem, Kummer's theory of divisibility, lattice, permissible lattice, critical determinants and lattice, body, packing, lattice packing set, packing lattice, ray function, star body, Hermite's constant.
Received: 28.03.2016
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, Volume 60, Issue 10, Pages 77–81
DOI: https://doi.org/10.3103/S1066369X16100133
Bibliographic databases:
Document Type: Article
UDC: 511.682
Language: Russian
Citation: Zh. N. Temirgaliyeva, N. Temirgaliyev, ““Geometry of numbers” in a context of algebraic theory of numbers”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 10, 92–97; Russian Math. (Iz. VUZ), 60:10 (2016), 77–81
Citation in format AMSBIB
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\paper ``Geometry of numbers'' in a~context of algebraic theory of numbers
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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