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Lecture notes on geometry of numbers

Hans-Gill, R. J.

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Lecture notes on geometry of numbers

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Lecture notes on geometry of numbers/ by R. J. Hans-Gill, Madhu Raka, Ranjeet Sehmi.
作者:	Hans-Gill, R. J.
其他作者:	Raka, Madhu.
出版者:	Singapore :Springer Nature Singapore : : 2024.,
面頁冊數:	x, 207 p. :ill. (some col.), digital ;24 cm.
內容註:	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.
Contained By:	Springer Nature eBook
標題:	Geometry of numbers. -
電子資源:	https://doi.org/10.1007/978-981-99-9602-5
ISBN:	9789819996025

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

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

523798
Geometry of numbers.

LC Class. No.: QA241.5

Dewey Class. No.: 512.75

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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.
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