LEADER 03129nam 22005415 450 001 9910874686703321 005 20240714125730.0 010 $a9789819996025$b(electronic bk.) 010 $z9789819996018 024 7 $a10.1007/978-981-99-9602-5 035 $a(MiAaPQ)EBC31527404 035 $a(Au-PeEL)EBL31527404 035 $a(CKB)32813229100041 035 $a(DE-He213)978-981-99-9602-5 035 $a(EXLCZ)9932813229100041 100 $a20240713d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLecture Notes on Geometry of Numbers /$fby R. J. Hans-Gill, Madhu Raka, Ranjeet Sehmi 205 $a1st ed. 2024. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2024. 215 $a1 online resource (212 pages) 225 1 $aUniversity Texts in the Mathematical Sciences,$x2731-9326 311 08$aPrint version: Hans-Gill, R. J. Lecture Notes on Geometry of Numbers Singapore : Springer,c2024 9789819996018 327 $a1. 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. 330 $aThis book serves as an illuminating introduction to the intricacies of the geometry of numbers. It commences by exploring basic concepts of convex sets and lattices in Euclidean space and goes on to delve into Minkowski?s fundamental theorem for convex bodies and its applications. It discusses critical determinants and successive minima before explaining the core results of packings and coverings. The text goes on to delve into the significance of renowned conjectures such as Minkowski?s conjecture regarding the product of linear forms, Watson?s conjecture, and the conjecture of Bambah, Dumir, and Hans-Gill concerning non-homogeneous minima of indefinite quadratic forms. Dedicated to Prof. R.P. Bambah on his 98th birthday, a living legend of number theory in India, this comprehensive book addresses both homogeneous and non-homogeneous problems, while sprinkling in historical insights and highlighting unresolved questions in the field. It is ideally suited for beginners embarking on self-study as well as for use as a text for a one- or two-semester introductory course. . 410 0$aUniversity Texts in the Mathematical Sciences,$x2731-9326 606 $aNumber theory 606 $aAlgebraic geometry 606 $aNumber Theory 606 $aAlgebraic Geometry 615 0$aNumber theory. 615 0$aAlgebraic geometry. 615 14$aNumber Theory. 615 24$aAlgebraic Geometry. 676 $a512.75 700 $aHans-Gill$b R. J$01749541 701 $aRaka$b Madhu$01749542 701 $aSehmi$b Ranjeet$01749543 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910874686703321 996 $aLecture Notes on Geometry of Numbers$94183819 997 $aUNINA