Lecture Notes on Geometry of Numbers

• Verfasst von: Hans-Gill, R. J. [VerfasserIn]
• Verfasst von: Raka, Madhu [VerfasserIn]
• Verfasst von: Sehmi, Ranjeet [VerfasserIn]
• Titel: Lecture Notes on Geometry of Numbers
• Verf.angabe: by R. J. Hans-Gill, Madhu Raka, Ranjeet Sehmi
• Ausgabe: 1st ed. 2024.
• Verlagsort: Singapore
• Verlagsort: Singapore
• Verlag: Springer Nature Singapore
• Verlag: Imprint: Springer
• E-Jahr: 2024
• Jahr: 2024.
• Jahr: 2024.
• Umfang: 1 Online-Ressource(X, 207 p. 23 illus., 2 illus. in color.)
• Gesamttitel/Reihe: University Texts in the Mathematical Sciences
• ISBN: 978-981-9996-02-5
• DOI: doi:10.1007/978-981-99-9602-5
• Datenträger: Online-Ressource
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe: Hans-Gill, R. J., 1943 - : Lecture notes on geometry of numbers. - Singapore : Springer Nature Singapore, 2024. - x, 207 Seiten
• K10plus-PPN: 1895508614
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

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.

Abstract

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. .