Integral Quadratic Forms And Lattices
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Integral Quadratic Forms And Lattices
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Author : Myung-Hwan Kim
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Integral Quadratic Forms And Lattices written by Myung-Hwan Kim and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This volume presents the proceedings of an international conference held at Seoul National University (Korea). Talks covered recent developments in diverse areas related to the theory of integral quadratic forms and hermitian forms, local densities, linear relations and congruences of theta series, zeta functions of prehomogeneous vector spaces, lattices with maximal finite matrix groups, globally irreducible lattices, Mordell-Weil lattices, and more. Articles in the volume represent expository lectures by leading experts on recent developments in the field. The book offers a comprehensive introduction to the current state of knowledge in the arithmetic theory of quadratic forms and provides active directions of research with new results. Topics addressed in the volume emphasize connections with related fields, such as group theory, arithmetic geometry, analytic number theory, and modular forms. The book is an excellent introductory guide for students as well as a rich reference source for researchers.
Introduction To Quadratic Forms
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Author : O. Timothy O'Meara
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-12-14
Introduction To Quadratic Forms written by O. Timothy O'Meara and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-12-14 with Mathematics categories.
From the reviews: "Anyone who has heard O'Meara lecture will recognize in every page of this book the crispness and lucidity of the author's style. [...] The organization and selection of material is superb. [...] deserves high praise as an excellent example of that too-rare type of mathematical exposition combining conciseness with clarity." Bulletin of the AMS
Diophantine Methods Lattices And Arithmetic Theory Of Quadratic Forms
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Author : Wai Kiu Chan
language : en
Publisher: American Mathematical Soc.
Release Date : 2013
Diophantine Methods Lattices And Arithmetic Theory Of Quadratic Forms written by Wai Kiu Chan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
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.
Sphere Packings Lattices And Groups
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Author : John Conway
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Sphere Packings Lattices And Groups written by John Conway and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
We now apply the algorithm above to find the 121 orbits of norm -2 vectors from the (known) nann 0 vectors, and then apply it again to find the 665 orbits of nann -4 vectors from the vectors of nann 0 and -2. The neighbors of a strictly 24 dimensional odd unimodular lattice can be found as follows. If a norm -4 vector v E II . corresponds to the sum 25 1 of a strictly 24 dimensional odd unimodular lattice A and a !-dimensional lattice, then there are exactly two nonn-0 vectors of ll25,1 having inner product -2 with v, and these nann 0 vectors correspond to the two even neighbors of A. The enumeration of the odd 24-dimensional lattices. Figure 17.1 shows the neighborhood graph for the Niemeier lattices, which has a node for each Niemeier lattice. If A and B are neighboring Niemeier lattices, there are three integral lattices containing A n B, namely A, B, and an odd unimodular lattice C (cf. [Kne4]). An edge is drawn between nodes A and B in Fig. 17.1 for each strictly 24-dimensional unimodular lattice arising in this way. Thus there is a one-to-one correspondence between the strictly 24-dimensional odd unimodular lattices and the edges of our neighborhood graph. The 156 lattices are shown in Table 17 .I. Figure I 7. I also shows the corresponding graphs for dimensions 8 and 16.
Sphere Packings Lattices And Groups
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Author : John H. Conway
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Sphere Packings Lattices And Groups written by John H. Conway and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
The main themes. This book is mainly concerned with the problem of packing spheres in Euclidean space of dimensions 1,2,3,4,5, . . . . Given a large number of equal spheres, what is the most efficient (or densest) way to pack them together? We also study several closely related problems: the kissing number problem, which asks how many spheres can be arranged so that they all touch one central sphere of the same size; the covering problem, which asks for the least dense way to cover n-dimensional space with equal overlapping spheres; and the quantizing problem, important for applications to analog-to-digital conversion (or data compression), which asks how to place points in space so that the average second moment of their Voronoi cells is as small as possible. Attacks on these problems usually arrange the spheres so their centers form a lattice. Lattices are described by quadratic forms, and we study the classification of quadratic forms. Most of the book is devoted to these five problems. The miraculous enters: the E 8 and Leech lattices. When we investigate those problems, some fantastic things happen! There are two sphere packings, one in eight dimensions, the E 8 lattice, and one in twenty-four dimensions, the Leech lattice A , which are unexpectedly good and very 24 symmetrical packings, and have a number of remarkable and mysterious properties, not all of which are completely understood even today.
Automorphic Forms And Even Unimodular Lattices
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Author : Gaëtan Chenevier
language : en
Publisher: Springer
Release Date : 2019-02-28
Automorphic Forms And Even Unimodular Lattices written by Gaëtan Chenevier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-28 with Mathematics categories.
This book includes a self-contained approach of the general theory of quadratic forms and integral Euclidean lattices, as well as a presentation of the theory of automorphic forms and Langlands' conjectures, ranging from the first definitions to the recent and deep classification results due to James Arthur. Its connecting thread is a question about lattices of rank 24: the problem of p-neighborhoods between Niemeier lattices. This question, whose expression is quite elementary, is in fact very natural from the automorphic point of view, and turns out to be surprisingly intriguing. We explain how the new advances in the Langlands program mentioned above pave the way for a solution. This study proves to be very rich, leading us to classical themes such as theta series, Siegel modular forms, the triality principle, L-functions and congruences between Galois representations. This monograph is intended for any mathematician with an interest in Euclidean lattices, automorphic forms or number theory. A large part of it is meant to be accessible to non-specialists.
Algebraic And Arithmetic Theory Of Quadratic Forms
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Author : Ricardo Baeza
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Algebraic And Arithmetic Theory Of Quadratic Forms written by Ricardo Baeza and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
This proceedings volume contains papers presented at the International Conference on the algebraic and arithmetic theory of quadratic forms held in Talca (Chile). The modern theory of quadratic forms has connections with a broad spectrum of mathematical areas including number theory, geometry, and K-theory. This volume contains survey and research articles covering the range of connections among these topics. The survey articles bring readers up-to-date on research and open problems in representation theory of integral quadratic forms, the algebraic theory of finite square class fields, and developments in the theory of Witt groups of triangulated categories. The specialized articles present important developments in both the algebraic and arithmetic theory of quadratic forms, as well as connections to geometry and K-theory. The volume is suitable for graduate students and research mathematicians interested in various aspects of the theory of quadratic forms.
Arithmetic Of Quadratic Forms
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Author : Yoshiyuki Kitaoka
language : en
Publisher: Cambridge University Press
Release Date : 1999-04-29
Arithmetic Of Quadratic Forms written by Yoshiyuki Kitaoka and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-04-29 with Mathematics categories.
Provides an introduction to quadratic forms.
The Sensual Quadratic Form
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Author : John Horton Conway
language : en
Publisher: American Mathematical Soc.
Release Date : 1997-12-31
The Sensual Quadratic Form written by John Horton Conway and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-12-31 with Mathematics categories.
John Horton Conway's unique approach to quadratic forms was the subject of the Hedrick Lectures that he gave in August of 1991 at the Joint Meetings of the Mathematical Association of America and the American Mathematical Society in Orono, Maine. This book presents the substance of those lectures. The book should not be thought of as a serious textbook on the theory of quadratic forms. It consists rather of a number of essays on particular aspects of quadratic forms that have interested the author. The lectures are self-contained and will be accessible to the generally informed reader who has no particular background in quadratic form theory. The minor exceptions should not interrupt the flow of ideas. The afterthoughts to the lectures contain discussion of related matters that occasionally presuppose greater knowledge.
Rational Quadratic Forms
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Author : J. W. S. Cassels
language : en
Publisher: Courier Dover Publications
Release Date : 2008-08-08
Rational Quadratic Forms written by J. W. S. Cassels and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-08 with Mathematics categories.
Exploration of quadratic forms over rational numbers and rational integers offers elementary introduction. Covers quadratic forms over local fields, forms with integral coefficients, reduction theory for definite forms, more. 1968 edition.