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008			240724s2013 xx o ||||0 eng d
020			_a9780821895030 _q(electronic bk.)
020			_z9780821883181
035			_a(MiAaPQ)EBC3113275
035			_a(Au-PeEL)EBL3113275
035			_a(CaPaEBR)ebr10878730
035			_a(OCoLC)834150003
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA179 -- .I58 2013eb
082	0		_a512.7/4
100	1		_aChan, Wai Kiu.
245	1	0	_aDiophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2013.
264		4	_c©2013.
300			_a1 online resource (258 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aContemporary Mathematics ; _vv.587
505	0		_aIntro -- In Memoriam -- Contents -- Preface -- Boris Venkov's Theory of Lattices and Spherical Designs -- 1. Introduction -- 2. Lattices, designs and modular forms -- 3. Lattices and spherical designs -- 4. Unimodular lattices -- 5. Tight spherical designs -- 6. Hecke operators -- References -- Generalized Theta Series and Spherical Designs -- 1. Introduction -- 2. The generalized theta series Θ_{ , } -- 3. Characterizations of -designs -- 4. Root lattices | ADE -- 5. The Leech lattice Λ₂₄ -- References -- Representations of integral quadratic polynomials -- 1. Introduction -- 2. Universal Ternary Quadratic Polynomials -- 3. Regular Ternary Triangular Forms -- 4. Representations of Cosets -- References -- Dense lattices as Hermitian tensor products -- 1. Introduction -- 2. Tensor products over ℤ -- 3. Preliminaries on Hermitian lattices -- 4. Hermitian ℤ[(1+√-11)/2]-lattices. -- 5. Hermitian ℤ[(1+√-7)/2]-lattices. -- References -- Small zeros of homogeneous cubic congruences -- 1. Introduction -- Acknowledgement -- 2. Quaternary cubic forms having no small zeros -- 3. Preparations -- 4. An application of Bertini's Theorem -- 5. Proofs of Theorems 1.2 and 1.3 -- References -- Strictly Regular Diagonal Positive Definite Quaternary Integral Quadratic Forms -- 1. Introduction -- 2. Infinite families of diagonal regular quaternary lattices -- 3. Candidates for strict regularity -- References -- Heights and quadratic forms: Cassels' theorem and its generalizations -- 1. Introduction: Cassels' theorem -- 2. Notation and heights -- 3. Extensions over global fields -- 4. Multiple zeros and isotropic subspaces -- 5. Effective structure theorems -- 6. Effective results with additional conditions -- 7. Open problems -- Acknowledgment -- References -- On the positive integers satisfying the equation _{ }= ²+ ² -- 1. Introduction.
505	8		_a2. Preliminary results -- 3. The proof of Theorem 1.1 -- 4. Comments -- Acknowledgements. -- References -- Algorithms for computing maximal lattices in bilinear (and quadratic) spaces over number fields -- 1. Introduction and Notation -- 2. Duality for Bilinear Lattices -- 3. Maximal Bilinear Lattices -- 4. Maximal Quadratic Lattices -- 5. Neighbors and Genera -- References -- -adic Zeros of Systems of Quadratic Forms -- References -- The Number of Function Fields with Given Genus -- Introduction -- Notation and Auxiliary Results -- Proof of the Theorem -- References -- Unique Factorization in the Theory of Quadratic Forms -- 1. Theorem Statement -- 2. Proof of Key Case -- 3. Proof of Remaining Cases -- References -- Golden lattices -- 1. Introduction -- 2. Hilbert theta series of golden lattices -- 3. Examples -- References -- The extremal lattice of dimension 14, level 7 and its genus -- 1. Background on extremal lattices and modular forms -- 2. The extremal 7-modular lattice -- 3. Properties of the genus \ ₁₄(7⁺⁷) -- 4. Weakening the condition of extremality -- Acknowledgment -- References -- Strict Periodic Extreme Lattices -- 1. Introduction -- 2. A parameter space for periodic sets -- 3. Characterizing strict periodic extreme sets -- References -- Exceptional units and cyclic resultants, II -- 1. Introduction -- 2. Preliminary lemmas -- 3. Proof of Theorem 1.1 -- 4. Proof of Theorem 1.2 -- 5. Proof of Theorem 1.3 -- 6. Computations for small degrees -- References -- A note on generators of number fields -- 1. Introduction -- 2. Preliminaries -- 3. Proof of Theorem 1.2 -- 4. A general strategy -- 5. Application of Chebotarev's density theorem and GRH -- 6. Proof of Theorem 1.3 -- 7. The field ℚ(√-163) -- References -- Voronoï's reduction theory of _{ } over a totally real number field -- Introduction -- 1. Preliminaries.
505	8		_a2. Voronoï's algorithm of Λ₀-perfect forms -- 3. Polyhedral reduction of _{ }( _{ })/ (Λ₀)* -- 4. Ryshkov polyhedra of real quadratic fields -- References -- Some comments about Indefinite LLL -- 1. Review of LLL -- Acknowledgments -- 2. Quadratic equations -- 3. Back to indefinite LLL -- References.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aLinear algebraic groups -- Congresses.
650		0	_aForms, Quadratic -- Congresses.
650		0	_aNumber theory -- Congresses.
655		4	_aElectronic books.
700	1		_aFukshansky, Lenny.
700	1		_aSchulze-Pillot, Rainer.
700	1		_aVaaler, Jeffrey D.
776	0	8	_iPrint version: _aChan, Wai Kiu _tDiophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms _dProvidence : American Mathematical Society,c2013 _z9780821883181
797	2		_aProQuest (Firm)
830		0	_aContemporary Mathematics
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3113275 _zClick to View
999			_c68809 _d68809