Geometry of numbers

Geometry of numbers is the part of number theory which uses geometry for the study of algebraic numbers. Typically, a ring of algebraic integers is viewed as a lattice in $\mathbb {R} ^{n},$ and the study of these lattices provides fundamental information on algebraic numbers.^[1] Hermann Minkowski (1896) initiated this line of research at the age of 26 in his work The Geometry of Numbers.^[2]

The geometry of numbers has a close relationship with other fields of mathematics, especially functional analysis and Diophantine approximation, the problem of finding rational numbers that approximate an irrational quantity.^[3]

^ MSC classification, 2010, available at http://www.ams.org/msc/msc2010.html, Classification 11HXX.
^ Minkowski, Hermann (2013-08-27). Space and Time: Minkowski's papers on relativity. Minkowski Institute Press. ISBN 978-0-9879871-1-2.
^ Schmidt's books. Grötschel, Martin; Lovász, László; Schrijver, Alexander (1993), Geometric algorithms and combinatorial optimization, Algorithms and Combinatorics, vol. 2 (2nd ed.), Springer-Verlag, Berlin, doi:10.1007/978-3-642-78240-4, ISBN 978-3-642-78242-8, MR 1261419

[1] MSC classification, 2010, available at http://www.ams.org/msc/msc2010.html, Classification 11HXX.

[2] Minkowski, Hermann (2013-08-27). Space and Time: Minkowski's papers on relativity. Minkowski Institute Press. ISBN 978-0-9879871-1-2.

[3] Schmidt's books. Grötschel, Martin; Lovász, László; Schrijver, Alexander (1993), Geometric algorithms and combinatorial optimization, Algorithms and Combinatorics, vol. 2 (2nd ed.), Springer-Verlag, Berlin, doi:10.1007/978-3-642-78240-4, ISBN 978-3-642-78242-8, MR 1261419

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