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020 _a9789819996025
_9978-981-99-9602-5
024 7 _a10.1007/978-981-99-9602-5
_2doi
050 4 _aQA241-247.5
072 7 _aPBH
_2bicssc
072 7 _aMAT022000
_2bisacsh
072 7 _aPBH
_2thema
100 1 _aHans-Gill, R. J.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_980544
245 1 0 _aLecture Notes on Geometry of Numbers
_h[electronic resource] /
_cby R. J. Hans-Gill, Madhu Raka, Ranjeet Sehmi.
250 _a1st ed. 2024.
264 1 _aSingapore :
_bSpringer Nature Singapore :
_bImprint: Springer,
_c2024.
300 _aX, 207 p. 23 illus., 2 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aUniversity Texts in the Mathematical Sciences,
_x2731-9326
505 0 _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.
520 _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. .
650 0 _aNumber theory.
650 0 _aAlgebraic geometry.
650 1 4 _aNumber Theory.
650 2 4 _aAlgebraic Geometry.
700 1 _aRaka, Madhu.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_980545
700 1 _aSehmi, Ranjeet.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_980546
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9789819996018
776 0 8 _iPrinted edition:
_z9789819996032
776 0 8 _iPrinted edition:
_z9789819996049
830 0 _aUniversity Texts in the Mathematical Sciences,
_x2731-9326
_971590
856 4 0 _uhttps://doi.org/10.1007/978-981-99-9602-5
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c61587
_d61587