Lattices and the Geometry of Numbers
Keyword(s):
In this paper, we discuss the properties of lattices and their application in theoretical and algorithmic number theory. This result of Minkowski regarding the lattices initiated the subject of Geometry of Numbers, which uses geometry to study the properties of algebraic numbers. It has an application in various other fields of mathematics especially the study of Diophantine equations, analysis of functional analysis, etc. This paper gives an elementary introduction to the field of the geometry of numbers. In this paper, we shall first give a broad overview of the concept of lattice and then discuss the geometrical properties it has and its applications.
1971 ◽
Vol 69
(1)
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pp. 157-161
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2007 ◽
Vol 91
(522)
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pp. 453-461
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2018 ◽
Vol 36
(4)
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pp. 23-32
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2014 ◽
Vol 372
(2007)
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pp. 20120508
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1917 ◽
Vol 36
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pp. 61-83
2020 ◽
Vol 69
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pp. 225-246
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