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Theta Functions Elliptic Functions And
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Book Synopsis Theta Functions, Elliptic Functions and [pi] by : Heng Huat Chan
Download or read book Theta Functions, Elliptic Functions and [pi] written by Heng Huat Chan and published by de Gruyter. This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents several results on elliptic functions and Pi, using Jacobi's triple product identity as a tool to show suprising connections between different topics within number theory such as theta functions, Eisenstein series, the Dedekind delta function, and Ramanujan's work on Pi. The included exercises make it ideal for both classroom use and self-study.
Book Synopsis Theta functions, elliptic functions and π by : Heng Huat Chan
Download or read book Theta functions, elliptic functions and π written by Heng Huat Chan and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-07-06 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents several results on elliptic functions and Pi, using Jacobi’s triple product identity as a tool to show suprising connections between different topics within number theory such as theta functions, Eisenstein series, the Dedekind delta function, and Ramanujan’s work on Pi. The included exercises make it ideal for both classroom use and self-study.
Book Synopsis A Brief Introduction to Theta Functions by : Richard Bellman
Download or read book A Brief Introduction to Theta Functions written by Richard Bellman and published by Courier Corporation. This book was released on 2013-01-01 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published: New York: Rinehart and Winston, 1961.
Author :Komaravolu Chandrasekharan Publisher :Springer Science & Business Media ISBN 13 :3642522440 Total Pages :199 pages Book Rating :4.6/5 (425 download)
Book Synopsis Elliptic Functions by : Komaravolu Chandrasekharan
Download or read book Elliptic Functions written by Komaravolu Chandrasekharan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has grown out of a course of lectures on elliptic functions, given in German, at the Swiss Federal Institute of Technology, Zurich, during the summer semester of 1982. Its aim is to give some idea of the theory of elliptic functions, and of its close connexion with theta-functions and modular functions, and to show how it provides an analytic approach to the solution of some classical problems in the theory of numbers. It comprises eleven chapters. The first seven are function-theoretic, and the next four concern arithmetical applications. There are Notes at the end of every chapter, which contain references to the literature, comments on the text, and on the ramifications, old and new, of the problems dealt with, some of them extending into cognate fields. The treatment is self-contained, and makes no special demand on the reader's knowledge beyond the elements of complex analysis in one variable, and of group theory.
Download or read book Elliptic Functions written by Serge Lang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elliptic functions parametrize elliptic curves, and the intermingling of the analytic and algebraic-arithmetic theory has been at the center of mathematics since the early part of the nineteenth century. The book is divided into four parts. In the first, Lang presents the general analytic theory starting from scratch. Most of this can be read by a student with a basic knowledge of complex analysis. The next part treats complex multiplication, including a discussion of Deuring's theory of l-adic and p-adic representations, and elliptic curves with singular invariants. Part three covers curves with non-integral invariants, and applies the Tate parametrization to give Serre's results on division points. The last part covers theta functions and the Kronecker Limit Formula. Also included is an appendix by Tate on algebraic formulas in arbitrary charactistic.
Book Synopsis Ramanujan's Theta Functions by : Shaun Cooper
Download or read book Ramanujan's Theta Functions written by Shaun Cooper and published by Springer. This book was released on 2017-06-12 with total page 687 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theta functions were studied extensively by Ramanujan. This book provides a systematic development of Ramanujan’s results and extends them to a general theory. The author’s treatment of the subject is comprehensive, providing a detailed study of theta functions and modular forms for levels up to 12. Aimed at advanced undergraduates, graduate students, and researchers, the organization, user-friendly presentation, and rich source of examples, lends this book to serve as a useful reference, a pedagogical tool, and a stimulus for further research. Topics, especially those discussed in the second half of the book, have been the subject of much recent research; many of which are appearing in book form for the first time. Further results are summarized in the numerous exercises at the end of each chapter.
Book Synopsis Elliptic Functions and Elliptic Integrals by : Viktor Vasil_evich Prasolov
Download or read book Elliptic Functions and Elliptic Integrals written by Viktor Vasil_evich Prasolov and published by American Mathematical Soc.. This book was released on 1997-09-16 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the geometry and arithmetic of elliptic curves and to elliptic functions with applications to algebra and number theory. It includes modern interpretations of some famous classical algebraic theorems such as Abel's theorem on the lemniscate and Hermite's solution of the fifth degree equation by means of theta functions. Suitable as a text, the book is self-contained and assumes as prerequisites only the standard one-year courses of algebra and analysis.
Book Synopsis Elements of the Theory of Elliptic Functions by : Naum Ilʹich Akhiezer
Download or read book Elements of the Theory of Elliptic Functions written by Naum Ilʹich Akhiezer and published by American Mathematical Soc.. This book was released on 1990 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the theory of elliptic functions and its applications. Suitable primarily for engineers who work with elliptic functions, this work is also intended for those with background in the elements of mathematical analysis and the theory of functions contained in the first two years of mathematics and physics courses at the college level.
Book Synopsis Elliptic Functions and Elliptic Curves by : Patrick Du Val
Download or read book Elliptic Functions and Elliptic Curves written by Patrick Du Val and published by Cambridge University Press. This book was released on 1973-08-02 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive treatment of elliptic functions is linked by these notes to a study of their application to elliptic curves. This approach provides geometers with the opportunity to acquaint themselves with aspects of their subject virtually ignored by other texts. The exposition is clear and logically carries themes from earlier through to later topics. This enthusiastic work of scholarship is made complete with the inclusion of some interesting historical details and a very comprehensive bibliography.
Book Synopsis Tables of Theta-functions, Elliptic Integrals K and E, and Associated Coefficients in the Numerical Calculati on of Elliptic Functions by : Hantaro Nagaoka
Download or read book Tables of Theta-functions, Elliptic Integrals K and E, and Associated Coefficients in the Numerical Calculati on of Elliptic Functions written by Hantaro Nagaoka and published by . This book was released on 1922 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Elliptic Functions and Applications by : Derek F. Lawden
Download or read book Elliptic Functions and Applications written by Derek F. Lawden and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject matter of this book formed the substance of a mathematical se am which was worked by many of the great mathematicians of the last century. The mining metaphor is here very appropriate, for the analytical tools perfected by Cauchy permitted the mathematical argument to penetra te to unprecedented depths over a restricted region of its domain and enabled mathematicians like Abel, Jacobi, and Weierstrass to uncover a treasurehouse of results whose variety, aesthetic appeal, and capacity for arousing our astonishment have not since been equaled by research in any other area. But the circumstance that this theory can be applied to solve problems arising in many departments of science and engineering graces the topic with an additional aura and provides a powerful argument for including it in university courses for students who are expected to use mathematics as a tool for technological investigations in later life. Unfortunately, since the status of university staff is almost wholly determined by their effectiveness as research workers rather than as teachers, the content of undergraduate courses tends to reflect those academic research topics which are currently popular and bears little relationship to the future needs of students who are themselves not destined to become university teachers. Thus, having been comprehensively explored in the last century and being undoubtedly difficult .
Book Synopsis Ten Place Tables of the Jacobian Elliptic Functions by : Henry E. Fettis
Download or read book Ten Place Tables of the Jacobian Elliptic Functions written by Henry E. Fettis and published by . This book was released on 1966 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on Selected Topics in Mathematical Physics by : William A. Schwalm
Download or read book Lectures on Selected Topics in Mathematical Physics written by William A. Schwalm and published by Morgan & Claypool Publishers. This book was released on 2015-12-31 with total page 67 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a basic introduction to certain aspects of elliptic functions and elliptic integrals. Primarily, the elliptic functions stand out as closed solutions to a class of physical and geometrical problems giving rise to nonlinear differential equations. While these nonlinear equations may not be the types of greatest interest currently, the fact that they are solvable exactly in terms of functions about which much is known makes up for this. The elliptic functions of Jacobi, or equivalently the Weierstrass elliptic functions, inhabit the literature on current problems in condensed matter and statistical physics, on solitons and conformal representations, and all sorts of famous problems in classical mechanics. The lectures on elliptic functions have evolved as part of the first semester of a course on theoretical and mathematical methods given to first and second year graduate students in physics and chemistry at the University of North Dakota. They are for graduate students or for researchers who want an elementary introduction to the subject that nevertheless leaves them with enough of the details to address real problems. The style is supposed to be informal. The intention is to introduce the subject as a moderate extension of ordinary trigonometry in which the reference circle is replaced by an ellipse. This entre depends upon fewer tools and has seemed less intimidating that other typical introductions to the subject that depend on some knowledge of complex variables. The first three lectures assume only calculus, including the chain rule and elementary knowledge of differential equations. In the later lectures, the complex analytic properties are introduced naturally so that a more complete study becomes possible.
Book Synopsis Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory by : Johannes Blümlein
Download or read book Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory written by Johannes Blümlein and published by Springer. This book was released on 2019-01-30 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes review articles in the field of elliptic integrals, elliptic functions and modular forms intending to foster the discussion between theoretical physicists working on higher loop calculations and mathematicians working in the field of modular forms and functions and analytic solutions of higher order differential and difference equations.
Book Synopsis Algebraic Geometry and Theta Functions by : Arthur B. Coble
Download or read book Algebraic Geometry and Theta Functions written by Arthur B. Coble and published by American Mathematical Soc.. This book was released on 1929-12-31 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the result of extending and deepening all questions from algebraic geometry that are connected to the central problem of this book: the determination of the tritangent planes of a space curve of order six and genus four, which the author treated in his Colloquium Lecture in 1928 at Amherst. The first two chapters recall fundamental ideas of algebraic geometry and theta functions in such fashion as will be most helpful in later applications. In order to clearly present the state of the central problem, the author first presents the better-known cases of genus two (Chapter III) and genus three (Chapter IV). The case of genus four is discussed in the last chapter. The exposition is concise with a rich variety of details and references.
Book Synopsis Theory of Functions of a Complex Variable by : A. I. Markushevich
Download or read book Theory of Functions of a Complex Variable written by A. I. Markushevich and published by American Mathematical Soc.. This book was released on 2013 with total page 1178 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Explorations in Complex Functions by : Richard Beals
Download or read book Explorations in Complex Functions written by Richard Beals and published by Springer Nature. This book was released on 2020-10-19 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook explores a selection of topics in complex analysis. From core material in the mainstream of complex analysis itself, to tools that are widely used in other areas of mathematics, this versatile compilation offers a selection of many different paths. Readers interested in complex analysis will appreciate the unique combination of topics and connections collected in this book. Beginning with a review of the main tools of complex analysis, harmonic analysis, and functional analysis, the authors go on to present multiple different, self-contained avenues to proceed. Chapters on linear fractional transformations, harmonic functions, and elliptic functions offer pathways to hyperbolic geometry, automorphic functions, and an intuitive introduction to the Schwarzian derivative. The gamma, beta, and zeta functions lead into L-functions, while a chapter on entire functions opens pathways to the Riemann hypothesis and Nevanlinna theory. Cauchy transforms give rise to Hilbert and Fourier transforms, with an emphasis on the connection to complex analysis. Valuable additional topics include Riemann surfaces, steepest descent, tauberian theorems, and the Wiener–Hopf method. Showcasing an array of accessible excursions, Explorations in Complex Functions is an ideal companion for graduate students and researchers in analysis and number theory. Instructors will appreciate the many options for constructing a second course in complex analysis that builds on a first course prerequisite; exercises complement the results throughout.
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