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Lecture notes on geometry of numbers

Record Type:	Electronic resources : Monograph/item
Title/Author:	Lecture notes on geometry of numbersby R. J. Hans-Gill, Madhu Raka, Ranjeet Sehmi.
Author:	Hans-Gill, R. J.
other author:	Raka, Madhu.
Published:	Singapore :Springer Nature Singapore :2024.
Description:	x, 207 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Geometry of numbers.
Online resource:	https://doi.org/10.1007/978-981-99-9602-5
ISBN:	9789819996025$q(electronic bk.)

Lecture notes on geometry of numbers
Hans-Gill, R. J.

Lecture notes on geometry of numbers[electronic resource] /by R. J. Hans-Gill, Madhu Raka, Ranjeet Sehmi. - Singapore :Springer Nature Singapore :2024. - x, 207 p. :ill. (some col.), digital ;24 cm. - University texts in the mathematical sciences,2731-9326. - University texts in the mathematical sciences..

1. Preliminaries -- 2. Minkowski's Fundamental Theorem and its Applications -- 3. Lattices -- 4. Minima of Positive De nite Quadratic Forms -- 5. Critical Determinant -- 6. Successive Minima -- 7. Packings Density -- 8. Coverings -- 9. Homogeneous Minimum -- 10. Inhomogeneous Problems.

This book serves as an illuminating introduction to the intricacies of the geometry of numbers. It commences by exploring basic concepts of convex sets and lattices in Euclidean space and goes on to delve into Minkowski's fundamental theorem for convex bodies and its applications. It discusses critical determinants and successive minima before explaining the core results of packings and coverings. The text goes on to delve into the significance of renowned conjectures such as Minkowski's conjecture regarding the product of linear forms, Watson's conjecture, and the conjecture of Bambah, Dumir, and Hans-Gill concerning non-homogeneous minima of indefinite quadratic forms. Dedicated to Prof. R.P. Bambah on his 98th birthday, a living legend of number theory in India, this comprehensive book addresses both homogeneous and non-homogeneous problems, while sprinkling in historical insights and highlighting unresolved questions in the field. It is ideally suited for beginners embarking on self-study as well as for use as a text for a one- or two-semester introductory course.

ISBN: 9789819996025$q(electronic bk.)

Standard No.: 10.1007/978-981-99-9602-5doiSubjects--Topical Terms:

663201
Geometry of numbers.

LC Class. No.: QA241.5

Dewey Class. No.: 512.75

Lecture notes on geometry of numbers
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245 1 0 $a Lecture notes on geometry of numbers $h [electronic resource] / $c by R. J. Hans-Gill, Madhu Raka, Ranjeet Sehmi.
260 $a Singapore : $b Springer Nature Singapore : $b Imprint: Springer, $c 2024.
300 $a x, 207 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a University texts in the mathematical sciences, $x 2731-9326
505 0 $a 1. Preliminaries -- 2. Minkowski's Fundamental Theorem and its Applications -- 3. Lattices -- 4. Minima of Positive De nite Quadratic Forms -- 5. Critical Determinant -- 6. Successive Minima -- 7. Packings Density -- 8. Coverings -- 9. Homogeneous Minimum -- 10. Inhomogeneous Problems.
520 $a This book serves as an illuminating introduction to the intricacies of the geometry of numbers. It commences by exploring basic concepts of convex sets and lattices in Euclidean space and goes on to delve into Minkowski's fundamental theorem for convex bodies and its applications. It discusses critical determinants and successive minima before explaining the core results of packings and coverings. The text goes on to delve into the significance of renowned conjectures such as Minkowski's conjecture regarding the product of linear forms, Watson's conjecture, and the conjecture of Bambah, Dumir, and Hans-Gill concerning non-homogeneous minima of indefinite quadratic forms. Dedicated to Prof. R.P. Bambah on his 98th birthday, a living legend of number theory in India, this comprehensive book addresses both homogeneous and non-homogeneous problems, while sprinkling in historical insights and highlighting unresolved questions in the field. It is ideally suited for beginners embarking on self-study as well as for use as a text for a one- or two-semester introductory course.
650 0 $a Geometry of numbers. $3 663201
650 1 4 $a Number Theory. $3 274059
650 2 4 $a Algebraic Geometry. $3 274807
700 1 $a Raka, Madhu. $3 980009
700 1 $a Sehmi, Ranjeet. $3 980010
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a University texts in the mathematical sciences. $3 975708
856 4 0 $u https://doi.org/10.1007/978-981-99-9602-5
950 $a Mathematics and Statistics (SpringerNature-11649)