Lecture Notes on Geometry of Numbers
Lecture Notes on Geometry of Numbers
English | 2024 | ISBN: 9819996015 | 217 Pages | PDF EPUB (True) | 23 MB
English | 2024 | ISBN: 9819996015 | 217 Pages | PDF EPUB (True) | 23 MB
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.