03444nam a22005415i 4500 978-981-99-9602-5 DE-He213 20251030112628.0 cr nn 008mamaa 240713s2024 si | s |||| 0|eng d 9789819996025 978-981-99-9602-5 10.1007/978-981-99-9602-5 doi QA241-247.5 PBH bicssc MAT022000 bisacsh PBH thema Hans-Gill, R. J. author. aut http://id.loc.gov/vocabulary/relators/aut 80544 Lecture Notes on Geometry of Numbers [electronic resource] / by R. J. Hans-Gill, Madhu Raka, Ranjeet Sehmi. 1st ed. 2024. Singapore : Springer Nature Singapore : Imprint: Springer, 2024. X, 207 p. 23 illus., 2 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda University Texts in the Mathematical Sciences, 2731-9326 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. . Number theory. Algebraic geometry. Number Theory. Algebraic Geometry. Raka, Madhu. author. aut http://id.loc.gov/vocabulary/relators/aut 80545 Sehmi, Ranjeet. author. aut http://id.loc.gov/vocabulary/relators/aut 80546 SpringerLink (Online service) Springer Nature eBook Printed edition: 9789819996018 Printed edition: 9789819996032 Printed edition: 9789819996049 University Texts in the Mathematical Sciences, 2731-9326 71590 https://doi.org/10.1007/978-981-99-9602-5 ZDB-2-SMA ZDB-2-SXMS 61587 61587