Elliptic Polynomials
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Elliptic Polynomials
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Author : J.S. Lomont
language : en
Publisher: CRC Press
Release Date : 2000-08-31
Elliptic Polynomials written by J.S. Lomont and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-08-31 with Mathematics categories.
A remarkable interplay exists between the fields of elliptic functions and orthogonal polynomials. In the first monograph to explore their connections, Elliptic Polynomials combines these two areas of study, leading to an interesting development of some basic aspects of each. It presents new material about various classes of polynomials and about the odd Jacobi elliptic functions and their inverses. The term elliptic polynomials refers to the polynomials generated by odd elliptic integrals and elliptic functions. In studying these, the authors consider such things as orthogonality and the construction of weight functions and measures, finding structure constants and interesting inequalities, and deriving useful formulas and evaluations. Although some of the material may be familiar, it establishes a new mathematical field that intersects with classical subjects at many points. Its wealth of information on important properties of polynomials and clear, accessible presentation make Elliptic Polynomials valuable to those in real and complex analysis, number theory, and combinatorics, and will undoubtedly generate further research.
Elliptic Orthogonal Polynomials
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Author : Carl John Rees
language : en
Publisher:
Release Date : 1945
Elliptic Orthogonal Polynomials written by Carl John Rees and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1945 with Functions, Orthogonal categories.
One Semester Of Elliptic Curves
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Author : Torsten Ekedahl
language : en
Publisher: European Mathematical Society
Release Date : 2006
One Semester Of Elliptic Curves written by Torsten Ekedahl and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
These lecture notes grew out of a one semester introductory course on elliptic curves given to an audience of computer science and mathematics students, and assume only minimal background knowledge. After having covered basic analytic and algebraic aspects, putting special emphasis on explaining the interplay between algebraic and analytic formulas, they go on to some more specialized topics. These include the $j$-function from an algebraic and analytic perspective, a discussion of elliptic curves over finite fields, derivation of recursion formulas for the division polynomials, the algebraic structure of the torsion points of an elliptic curve, complex multiplication, and modular forms. In an effort to motivate basic problems the book starts very slowly but considers some aspects such as modular forms of higher level which are not usually treated. It presents more than 100 exercises and a Mathematica TM notebook that treats a number of calculations involving elliptic curves. The book is aimed at students of mathematics with a general interest in elliptic curves but also at students of computer science interested in their cryptographic aspects.
Numerical Methods For Roots Of Polynomials Part Ii
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Author : J.M. McNamee
language : en
Publisher: Elsevier Inc. Chapters
Release Date : 2013-07-19
Numerical Methods For Roots Of Polynomials Part Ii written by J.M. McNamee and has been published by Elsevier Inc. Chapters this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-19 with Mathematics categories.
We deal here with low-degree polynomials, mostly closed-form solutions. We describe early and modern solutions of the quadratic, and potential errors in these. Again we give the early history of the cubic, and details of Cardan’s solution and Vieta’s trigonometric approach. We consider the discriminant, which decides what type of roots the cubic has. Then we describe several ways (both old and new) of solving the quartic, most of which involve first solving a “resolvent” cubic. The quintic cannot in general be solved by radicals, but can be solved in terms of elliptic or related functions. We describe an algorithm due to Kiepert, which transforms the quintic into a form having no or term; then into a form where the coefficients depend on a single parameter; and later another similar form. This last form can be solved in terms of Weierstrass elliptic and theta functions, and finally the various transformations reversed.
Arithmetical Properties Of The Elliptic Polynomials Arising From The Real Multiplication Of The Jacobi Functions
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Author : Morgan Ward
language : en
Publisher:
Release Date : 1950
Arithmetical Properties Of The Elliptic Polynomials Arising From The Real Multiplication Of The Jacobi Functions written by Morgan Ward and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1950 with Elliptic functions categories.
Lectures On Orthogonal Polynomials And Special Functions
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Author : Howard S. Cohl
language : en
Publisher: Cambridge University Press
Release Date : 2020-10-15
Lectures On Orthogonal Polynomials And Special Functions written by Howard S. Cohl 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 2020-10-15 with Mathematics categories.
Contains graduate-level introductions by international experts to five areas of research in orthogonal polynomials and special functions.
Introduction To Applied Algebraic Systems
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Author : Norman R Reilly
language : en
Publisher: Oxford University Press
Release Date : 2009-11-02
Introduction To Applied Algebraic Systems written by Norman R Reilly and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-02 with Mathematics categories.
This upper-level undergraduate textbook provides a modern view of algebra with an eye to new applications that have arisen in recent years. A rigorous introduction to basic number theory, rings, fields, polynomial theory, groups, algebraic geometry and elliptic curves prepares students for exploring their practical applications related to storing, securing, retrieving and communicating information in the electronic world. It will serve as a textbook for an undergraduate course in algebra with a strong emphasis on applications. The book offers a brief introduction to elementary number theory as well as a fairly complete discussion of major algebraic systems (such as rings, fields, and groups) with a view of their use in bar coding, public key cryptosystems, error-correcting codes, counting techniques, and elliptic key cryptography. This is the only entry level text for algebraic systems that includes an extensive introduction to elliptic curves, a topic that has leaped to prominence due to its importance in the solution of Fermats Last Theorem and its incorporation into the rapidly expanding applications of elliptic curve cryptography in smart cards. Computer science students will appreciate the strong emphasis on the theory of polynomials, algebraic geometry and Groebner bases. The combination of a rigorous introduction to abstract algebra with a thorough coverage of its applications makes this book truly unique.
Elliptic Orthogonal Polynomials
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Author : Carl John Rees
language : en
Publisher:
Release Date : 1949
Elliptic Orthogonal Polynomials written by Carl John Rees and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1949 with categories.
Mordell Weil Lattices
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Author : Matthias Schütt
language : en
Publisher: Springer Nature
Release Date : 2019-10-17
Mordell Weil Lattices written by Matthias Schütt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-17 with Mathematics categories.
This book lays out the theory of Mordell–Weil lattices, a very powerful and influential tool at the crossroads of algebraic geometry and number theory, which offers many fruitful connections to other areas of mathematics. The book presents all the ingredients entering into the theory of Mordell–Weil lattices in detail, notably, relevant portions of lattice theory, elliptic curves, and algebraic surfaces. After defining Mordell–Weil lattices, the authors provide several applications in depth. They start with the classification of rational elliptic surfaces. Then a useful connection with Galois representations is discussed. By developing the notion of excellent families, the authors are able to design many Galois representations with given Galois groups such as the Weyl groups of E6, E7 and E8. They also explain a connection to the classical topic of the 27 lines on a cubic surface. Two chapters deal with elliptic K3 surfaces, a pulsating area of recent research activity which highlights many central properties of Mordell–Weil lattices. Finally, the book turns to the rank problem—one of the key motivations for the introduction of Mordell–Weil lattices. The authors present the state of the art of the rank problem for elliptic curves both over Q and over C(t) and work out applications to the sphere packing problem. Throughout, the book includes many instructive examples illustrating the theory.
Partial Differential Operators And Mathematical Physics
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Author : Michael Demuth
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-05-01
Partial Differential Operators And Mathematical Physics written by Michael Demuth 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 1995-05-01 with Mathematics categories.