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Author: Wai Kiu Chan
Publisher: American Mathematical Soc.
Published: 2013
Total Pages: 259
ISBN-13: 0821883186
DOWNLOAD EBOOK →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.
Author: Burton W Jones
Publisher: American Mathematical Soc.
Published: 1950-12-31
Total Pages: 212
ISBN-13: 1614440107
DOWNLOAD EBOOK →This monograph presents the central ideas of the arithmetic theory of quadratic forms in self-contained form, assuming only knowledge of the fundamentals of matric theory and the theory of numbers. Pertinent concepts of p -adic numbers and quadratic ideals are introduced. It would have been possible to avoid these concepts, but the theory gains elegance as well as breadth by the introduction of such relationships. Some results, and many of the methods, are here presented for the first time. The development begins with the classical theory in the field of reals from the point of view of representation theory; for in these terms, many of the later objectives and methods may be revealed. The successive chapters gradually narrow the fields and rings until one has the tools at hand to deal with the classical problems in the ring of rational integers. The analytic theory of quadratic forms is not dealt with because of the delicate analysis involved. However, some of the more important results are stated and references are given.
Author: Johannes Buchmann
Publisher: Springer Science & Business Media
Published: 2007-06-22
Total Pages: 328
ISBN-13: 3540463682
DOWNLOAD EBOOK →The book deals with algorithmic problems related to binary quadratic forms. It uniquely focuses on the algorithmic aspects of the theory. The book introduces the reader to important areas of number theory such as diophantine equations, reduction theory of quadratic forms, geometry of numbers and algebraic number theory. The book explains applications to cryptography and requires only basic mathematical knowledge. The author is a world leader in number theory.
Author: Leonard Eugene Dickson
Publisher: Courier Corporation
Published: 2005-06-03
Total Pages: 325
ISBN-13: 0486442349
DOWNLOAD EBOOK →The three-volume series History of the Theory of Numbers is the work of the distinguished mathematician Leonard Eugene Dickson, who taught at the University of Chicago for four decades and is celebrated for his many contributions to number theory and group theory. This final volume in the series, which is suitable for upper-level undergraduates and graduate students, is devoted to quadratic and higher forms. It can be read independently of the preceding volumes, which explore divisibility and primality and diophantine analysis. Topics include reduction and equivalence of binary quadratic forms and representation of integers; composition of binary quadratic forms; the composition of orders and genera; irregular determinants; classes of binary quadratic forms with integral coefficients; binary quadratic forms whose coefficients are complete integers or integers of a field; classes of binary quadratic forms with complex integral coefficients; ternary and quaternary quadratic forms; cubic forms in three or more variables; binary hermitian forms; bilinear forms, matrices, and linear substitutions; congruencial theory of forms; and many other related topics. Indexes of authors cited and subjects appear at the end of the book.
Author: John Horton Conway
Publisher: Cambridge University Press
Published: 1997
Total Pages: 180
ISBN-13: 9780883850305
DOWNLOAD EBOOK →Quadratic forms are presented in a pictorial way, elucidating many topics in algebra, number theory and geometry.
Author: Krishnaswami Alladi
Publisher: Springer Science & Business Media
Published: 2013-08-13
Total Pages: 303
ISBN-13: 1461474884
DOWNLOAD EBOOK →In the last decade, the areas of quadratic and higher degree forms have witnessed dramatic advances. This volume is an outgrowth of three seminal conferences on these topics held in 2009, two at the University of Florida and one at the Arizona Winter School. The volume also includes papers from the two focused weeks on quadratic forms and integral lattices at the University of Florida in 2010.Topics discussed include the links between quadratic forms and automorphic forms, representation of integers and forms by quadratic forms, connections between quadratic forms and lattices, and algorithms for quaternion algebras and quadratic forms. The book will be of interest to graduate students and mathematicians wishing to study quadratic and higher degree forms, as well as to established researchers in these areas. Quadratic and Higher Degree Forms contains research and semi-expository papers that stem from the presentations at conferences at the University of Florida as well as survey lectures on quadratic forms based on the instructional workshop for graduate students held at the Arizona Winter School. The survey papers in the volume provide an excellent introduction to various aspects of the theory of quadratic forms starting from the basic concepts and provide a glimpse of some of the exciting questions currently being investigated. The research and expository papers present the latest advances on quadratic and higher degree forms and their connections with various branches of mathematics.
Author: Leonard Eugene Dickson
Publisher:
Published: 1923
Total Pages: 328
ISBN-13:
DOWNLOAD EBOOK →Author: Samuele Anni
Publisher: American Mathematical Soc.
Published: 2019-06-19
Total Pages: 286
ISBN-13: 147043525X
DOWNLOAD EBOOK →This volume contains the proceedings of the Building Bridges: 3rd EU/US Summer School and Workshop on Automorphic Forms and Related Topics, which was held in Sarajevo from July 11–22, 2016. The articles summarize material which was presented during the lectures and speed talks during the workshop. These articles address various aspects of the theory of automorphic forms and its relations with the theory of L-functions, the theory of elliptic curves, and representation theory. In addition to mathematical content, the workshop held a panel discussion on diversity and inclusion, which was chaired by a social scientist who has contributed to this volume as well. This volume is intended for researchers interested in expanding their own areas of focus, thus allowing them to “build bridges” to mathematical questions in other fields.
Author: John Horton Conway
Publisher: American Mathematical Soc.
Published: 1997-12-31
Total Pages: 152
ISBN-13: 1470448424
DOWNLOAD EBOOK →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.
Author: J. W. S. Cassels
Publisher: Courier Dover Publications
Published: 2008-08-08
Total Pages: 429
ISBN-13: 0486466701
DOWNLOAD EBOOK →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.
