Author: Andrew William HarrellPublisher:
ISBN:
Category :
Languages : en
Pages : 102
Book Description
On Voronoi's Method of Reducing Positive Definite Quadratic Forms
Author: Andrew William HarrellPublisher:
ISBN:
Category :
Languages : en
Pages : 102
Book Description
Computational Geometry of Positive Definite Quadratic Forms
Author: Achill SchurmannPublisher: American Mathematical Soc.
ISBN: 082184735X
Category : Mathematics
Languages : en
Pages : 183
Book Description
"Starting from classical arithmetical questions on quadratic forms, this book takes the reader step by step through the connections with lattice sphere packing and covering problems. As a model for polyhedral reduction theories of positive definite quadratic forms, Minkowski's classical theory is presented, including an application to multidimensional continued fraction expansions. The reduction theories of Voronoi are described in great detail, including full proofs, new views, and generalizations that cannot be found elsewhere. Based on Voronoi's second reduction theory, the local analysis of sphere coverings and several of its applications are presented. These include the classification of totally real thin number fields, connections to the Minkowski conjecture, and the discovery of new, sometimes surprising, properties of exceptional structures such as the Leech lattice or the root lattices." "Throughout this book, special attention is paid to algorithms and computability, allowing computer-assisted treatments. Although dealing with relatively classical topics that have been worked on extensively by numerous authors, this book is exemplary in showing how computers may help to gain new insights."--BOOK JACKET.
Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms
Author: Wai Kiu ChanPublisher: American Mathematical Soc.
ISBN: 0821883186
Category : Mathematics
Languages : en
Pages : 259
Book Description
This volume contains the proceedings of the International Workshop on Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms. The articles cover the arithmetic theory of quadratic forms and lattices, as well as the effective Diophantine analysis with height functions.
Voronoi Translated
Author: Georgi? Feodos?evich Vorono?Publisher: Lulu.com
ISBN: 9741315031
Category : Reference
Languages : en
Pages : 292
Book Description
Works by Dirichlet and Voronoi have been translated from German and French into English by Tiyapan. Also the latter have given a brief introduction to the study of Voronoi tessellation.Tiyapan graduated B.Sc. from Ramkhamhaeng University and B.Eng. from Chulalongkorn University, both in Thailand. He finished an M.Sc. at UMIST, England, began his Ph.D. study at Tokyo Institute of Technology and completed it at University of Manchester, England. His doctoral thesis (2004) was on Percolation and Voronoi Tessellation, namely percolation within percolation within Voronoi structures.These translations have been done during the beginning of his Ph.D. project in Manchester.
Second Memoir, Studies on the Primitive Parallelohedra, Second Part, Domain of Quadratic Forms
Author: G. F. VoronoiPublisher: Lulu.com
ISBN: 9748824918
Category : Reference
Languages : en
Pages : 136
Book Description
This is an English translation of the second part of the second memoir by Georges Fedosevich Voronoi, which appeared posthumously in 1909.Kit Tyabandha who translated this has a Ph.D. from University of Manchester in England. His thesis was related to percolation within percolation of Voronoi networks.
Computations with Modular Forms
Author: Gebhard BöcklePublisher: Springer Science & Business Media
ISBN: 3319038478
Category : Mathematics
Languages : en
Pages : 377
Book Description
This volume contains original research articles, survey articles and lecture notes related to the Computations with Modular Forms 2011 Summer School and Conference, held at the University of Heidelberg. A key theme of the Conference and Summer School was the interplay between theory, algorithms and experiment. The 14 papers offer readers both, instructional courses on the latest algorithms for computing modular and automorphic forms, as well as original research articles reporting on the latest developments in the field. The three Summer School lectures provide an introduction to modern algorithms together with some theoretical background for computations of and with modular forms, including computing cohomology of arithmetic groups, algebraic automorphic forms, and overconvergent modular symbols. The 11 Conference papers cover a wide range of themes related to computations with modular forms, including lattice methods for algebraic modular forms on classical groups, a generalization of the Maeda conjecture, an efficient algorithm for special values of p-adic Rankin triple product L-functions, arithmetic aspects and experimental data of Bianchi groups, a theoretical study of the real Jacobian of modular curves, results on computing weight one modular forms, and more.
Perfect Lattices in Euclidean Spaces
Author: Jacques MartinetPublisher: Springer Science & Business Media
ISBN: 3662051672
Category : Mathematics
Languages : en
Pages : 535
Book Description
Lattices are discrete subgroups of maximal rank in a Euclidean space. To each such geometrical object, we can attach a canonical sphere packing which, assuming some regularity, has a density. The question of estimating the highest possible density of a sphere packing in a given dimension is a fascinating and difficult problem: the answer is known only up to dimension 3. This book thus discusses a beautiful and central problem in mathematics, which involves geometry, number theory, coding theory and group theory, centering on the study of extreme lattices, i.e. those on which the density attains a local maximum, and on the so-called perfection property. Written by a leader in the field, it is closely related to, though disjoint in content from, the classic book by J.H. Conway and N.J.A. Sloane, Sphere Packings, Lattices and Groups, published in the same series as vol. 290. Every chapter except the first and the last contains numerous exercises. For simplicity those chapters involving heavy computational methods contain only few exercises. It includes appendices on Semi-Simple Algebras and Quaternions and Strongly Perfect Lattices.
C-types of N-dimensional Lattices and 5-dimensional Primitive Parallelohedra
Author: Sergeĭ Sergeevich RyshkovPublisher: American Mathematical Soc.
ISBN: 9780821830376
Category : Mathematics
Languages : en
Pages : 148
Book Description
Sphere Packings
Author: Chuanming ZongPublisher: Springer Science & Business Media
ISBN: 0387227806
Category : Mathematics
Languages : en
Pages : 245
Book Description
Sphere packings is one of the most fascinating and challenging subjects in mathematics. In the course of centuries, many exciting results have been obtained, ingenious methods created, related challenging problems proposed, and many surprising connections with other subjects found. This book gives a full account of this fascinating subject, especially its local aspects, discrete aspects, and its proof methods. The book includes both classical and contemporary results and provides a full treatment of the subject.
Author: Ross Evon Staffeldt