Composition Of Binary Quadratic Forms Over Integral Domains
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Composition Of Binary Quadratic Forms Over Integral Domains
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Author : Bill J. Dulin
language : en
Publisher:
Release Date : 1969
Composition Of Binary Quadratic Forms Over Integral Domains written by Bill J. Dulin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Forms, Binary categories.
Composition Of Binary Quadratic Forms Over Suprafinitive Integral Domains
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Author : Constance Jane Boyd
language : en
Publisher:
Release Date : 1966
Composition Of Binary Quadratic Forms Over Suprafinitive Integral Domains written by Constance Jane Boyd and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Forms, Binary categories.
Binary Quadratic Forms
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Author : Duncan A. Buell
language : en
Publisher: Springer Science & Business Media
Release Date : 1989-08-25
Binary Quadratic Forms written by Duncan A. Buell 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 1989-08-25 with Mathematics categories.
The first coherent exposition of the theory of binary quadratic forms was given by Gauss in the Disqnisitiones Arithmeticae. During the nine teenth century, as the theory of ideals and the rudiments of algebraic number theory were developed, it became clear that this theory of bi nary quadratic forms, so elementary and computationally explicit, was indeed just a special case of a much more elega,nt and abstract theory which, unfortunately, is not computationally explicit. In recent years the original theory has been laid aside. Gauss's proofs, which involved brute force computations that can be done in what is essentially a two dimensional vector space, have been dropped in favor of n-dimensional arguments which prove the general theorems of algebraic number the ory. In consequence, this elegant, yet pleasantly simple, theory has been neglected even as some of its results have become extremely useful in certain computations. I find this neglect unfortunate, because binary quadratic forms have two distinct attractions. First, the subject involves explicit computa tion and many of the computer programs can be quite simple. The use of computers in experimenting with examples is both meaningful and enjoyable; one can actually discover interesting results by com puting examples, noticing patterns in the "data," and then proving that the patterns result from the conclusion of some provable theorem.
The Shaping Of Arithmetic After C F Gauss S Disquisitiones Arithmeticae
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Author : Catherine Goldstein
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-02-03
The Shaping Of Arithmetic After C F Gauss S Disquisitiones Arithmeticae written by Catherine Goldstein 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 2007-02-03 with Mathematics categories.
Since its publication, C.F. Gauss's Disquisitiones Arithmeticae (1801) has acquired an almost mythical reputation, standing as an ideal of exposition in notation, problems and methods; as a model of organisation and theory building; and as a source of mathematical inspiration. Eighteen authors - mathematicians, historians, philosophers - have collaborated in this volume to assess the impact of the Disquisitiones, in the two centuries since its publication.
Selected Papers And Other Writings
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Author : Irving Kaplansky
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-04-13
Selected Papers And Other Writings written by Irving Kaplansky 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 1995-04-13 with Mathematics categories.
It is not often that one gets to write a preface to a collection of one's own papers. The most urgent task is to thank the people who made this book possible. That means first of all Hy Bass who, on behalf of Springer-Verlag, approached me about the idea. The late Walter Kaufmann-Biihler was very encouraging; Paulo Ribenboim helped in an important way; and Ina Lindemann saw the project through with tact and skill that I deeply appreciate. My wishes have been indulged in two ways. First, I was allowed to follow up each selected paper with an afterthought. Back in my student days I became aware of the Gesammelte Mathematische Werke of Dedekind, edited by Fricke, Noether, and Ore. I was impressed by the editors' notes that followed most of the papers and found them very usefuL A more direct model was furnished by the collected papers of Lars Ahlfors, in which the author himself supplied afterthoughts for each paper or group of papers. These were tough acts to follow, but I hope that some readers will find at least some of my afterthoughts interesting. Second, I was permitted to add eight previously unpublished items. My model here, to a certain extent, was the charming little book, A Mathematician's Miscel lany by J. E. Littlewood. In picking these eight I had quite a selection to make -from fourteen loose-leaf notebooks of such writings. Here again I hope that at least some will be found to be of interest.
Representations Of Integers As Sums Of Squares
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Author : E. Grosswald
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Representations Of Integers As Sums Of Squares written by E. Grosswald 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 2012-12-06 with Mathematics categories.
During the academic year 1980-1981 I was teaching at the Technion-the Israeli Institute of Technology-in Haifa. The audience was small, but con sisted of particularly gifted and eager listeners; unfortunately, their back ground varied widely. What could one offer such an audience, so as to do justice to all of them? I decided to discuss representations of natural integers as sums of squares, starting on the most elementary level, but with the inten tion of pushing ahead as far as possible in some of the different directions that offered themselves (quadratic forms, theory of genera, generalizations and modern developments, etc.), according to the interests of the audience. A few weeks after the start of the academic year I received a letter from Professor Gian-Carlo Rota, with the suggestion that I submit a manuscript for the Encyclopedia of Mathematical Sciences under his editorship. I answered that I did not have a ready manuscript to offer, but that I could use my notes on representations of integers by sums of squares as the basis for one. Indeed, about that time I had already started thinking about the possibility of such a book and had, in fact, quite precise ideas about the kind of book I wanted it to be.
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.
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.
Introduction To Quadratic Forms
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Author : O. Timothy O'Meara
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
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 2012-12-06 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
Ternary Quadratic Forms And Norms
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Author : O. Taussky
language : en
Publisher: CRC Press
Release Date : 2020-12-17
Ternary Quadratic Forms And Norms written by O. Taussky and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-17 with Mathematics categories.
This book covers topics including the Redei-Reichardt theorem, automorphs of ternary quadratic forms, facts concerning rational matrices leading to integral ternary forms representing zero, characteristics polynomials of symmetric matrices, and Gauss' theory of ternary quadratic forms.