# Elliptic functions and transcendence

by David William Masser

Publisher: Springer-Verlag in Berlin, New York

Written in English

## Subjects:

• Elliptic functions.,
• Transcendental numbers.

## Edition Notes

Bibliography: p. [141]-143.

Classifications The Physical Object Statement David Masser. Series Lecture notes in mathematics ; 437, Lecture notes in mathematics (Springer-Verlag) ;, 437. LC Classifications QA3 .L28 no. 437, QA343 .L28 no. 437 Pagination xiii, 143 p. ; Number of Pages 143 Open Library OL5065865M ISBN 10 0387071369 LC Control Number 74032365

McKean and Moll have written the nice book Elliptic Curves: Function Theory, Geometry, Arithmetic that cleanly illustrates the connection between elliptic curves and elliptic/modular functions. If you haven't seen the book already, you should. As for elliptic functions proper, my suggested books tend to be a bit on the old side, so pardon me if I don't know the newer treatments. Elliptic Functions: A Primer defines and describes what is an elliptic function, attempts to have a more elementary approach to them, and drastically reduce the complications of its classic formulae; from which the book proceeds to a more detailed study of the subject while being reasonably complete in itself. with particular emphasis on transcendence, algebraic independence and measures of the algebraic independence of numbers connected with exponential and elliptic functions. Special sections of the Introduction are devoted to period relations for Abelian varieties of CM-type, the author's results on the Schanuel conjecture. In complex analysis, an elliptic function is a meromorphic function that is periodic in two directions. Just as a periodic function of a real variable is defined by its values on an interval, an elliptic function is determined by its values on a fundamental parallelogram, which then repeat in a okto-atelier.com a doubly periodic function cannot be holomorphic, as it would then be a bounded entire.

Elliptic Functions A.1 Apology The excuse for these notes is the need I felt to collect together a concise number of formulae for elliptic functions in one coherent notation and from one constructive point of view. The idea is as much as possible to try to derive all possible identities from one single formula, or. We survey transcendence theory of values of elliptic functions in Section 3, linear independence in Section 4, and algebraic independence in Section 5. This splitting is somewhat artificial but convenient. Moreover, we restrict ourselves to elliptic functions, even when many results are only special cases of statements valid for abelian okto-atelier.com: Michel Waldschmidt. Transcendence of Elliptic Modular Functions in Characteristicp. Author links open overlay panel José Felipe Voloch *. Show moreCited by: 5. We survey transcendence theory of values of elliptic functions, linear independence and algebraic independence. This splitting is somewhat artificial but convenient. Moreover, we restrict ourselves to elliptic functions, even when many results are only special cases of statements valid for abelian functions.

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 . Jan 25,  · Free kindle book and epub digitized and proofread by Project Gutenberg. Elliptic Functions: An Elementary Text-Book for Students of Mathematics by Baker - Free Ebook Project GutenbergCited by: 2. I'm sorry if my question is trivial. In his book "Elements of the Theory of Elliptic Functions", page 44, Akhiezer proves, that any two elliptic functions with the same periods are connected by . Sep 25,  · Coverage of advanced topics: These include transcendental values of the following: elliptic functions, the j-function, modular forms, class group L-functions, and elliptic integrals. Transcendental results on both individual numbers as well as independence are presented.

## Elliptic functions and transcendence by David William Masser Download PDF EPUB FB2

Elliptic Functions and Transcendence (Lecture Notes in Mathematics) th Edition. by D.W. Masser (Author) ISBN ISBN Why is ISBN important. ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book.

Author: D.W. Masser. Elliptic Functions and Transcendence. Elliptic Functions and Transcendence. Authors; D. Masser; Book. 52 Citations; k Downloads; Part of the Lecture Notes in Mathematics book series (LNM, volume ) Log in to check access.

Buy eBook. USD Instant download; Readable on all devices; Own it forever Lemmas on elliptic functions with complex multiplication. Masser. Note: Citations are based on reference standards. However, formatting rules can vary widely between applications and fields of interest or study.

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Jul 08,  · We survey transcendence theory of values of elliptic functions in Section 3, linear independence in Section 4, and algebraic independence in Section 5. This splitting is somewhat artificial but convenient.

Moreover, we restrict ourselves to elliptic functions, even when many results are only special cases of statements valid for abelian okto-atelier.com by: 8.

Transcendence properties of modular functions have been studied by using their relations with periods of elliptic integrals; and untilall results about these modular functions were. elliptic integrals of the second kind, Weierstrass zeta function and extensions of an elliptic curve by G a.

He applies the so{called Schneider{Lang criterion to the Weierstrass elliptic and zeta functions and deduces the transcendence results due to Th.

Schneider on elliptic integrals of the rst and second kind. This introduction to the Jacobi elliptic, sn, cn, dn and related functions is parallel to the usual development of trigonometric functions, except that the unit circle is replaced by an ellipse.

These functions satisfy nonlinear differential equations that appear often in physical applications, for instance in particle mechanics. First we brieﬂy recall some of the basic transcendence results related to the exponential function (Section 1).

Next, in Section 2, we survey the main properties of elliptic functions that are involved in transcendence theory. We survey transcendence theory of values of elliptic functions Cited by: 8.

If we wish to ﬁnd the inverse of the elliptic integral x = sinφ = sn(u,k) or u = sn 0 dt. (1− t 2)(1− k2t) While there are 12 diﬀerent types of Jacobian elliptic functions based on the number of poles and the upper limit on the elliptic integral, the three most popular are the copolar trio of sine.

Higher Education and Professional Books. Mathematics and Science Books. Elliptic Functions and Transcendence (English, Paperback, Masser D.W.) Share. Elliptic Functions and Transcendence (English, Paperback, Masser D.W.) Be the first to Review this product ₹3, Jun 01,  · This book gives an introduction to some central results in transcendental number theory with application to periods and special values of modular and hypergeometric functions.

It also includes related results on Calabi–Yau manifolds. Most of the material is based on the author's own research and appears for the first time in book form. May 23,  · Elliptic Functions: A Primer defines and describes what is an elliptic function, attempts to have a more elementary approach to them, and drastically reduce the complications of its classic formulae; from which the book proceeds to a more detailed study of the subject while being reasonably complete in okto-atelier.com Edition: 1.

Keywords Transcendental numbers, elliptic functions, elliptic curves, elliptic integrals, algebraic independence, transcendence measures, measures of algebraic independence, Diophantine approxima-tion.

Mathematics Subject Classiﬁcation () 11G05 11J89 1 Exponential Function and Transcendence We start with a very brief list of some of.

in much more detail in a book, currently in preparation, based on various irrationality and transcendence proofs to the power series arising in mirror symmetry. Section 6 treats the theory of complex multiplication. Elliptic modular functions and modular forms are functions in H which are either invariant or transform in a speciﬁc way.

Chapter 1. Elliptic integrals and Jacobi’s theta functions 5 Elliptic integrals and the AGM: real case 5 Lemniscates and elastic curves 11 Euler’s addition theorem 18 Theta functions: preliminaries 24 Chapter 2. General theory of doubly periodic functions 31 Preliminaries 31 Periods of analytic functions 33 您的位置： 首页 > 科学自然 > 数学 > Elliptic Functions and Transcendence 目录导航.

elliptic functions are required to prove transcendence results and get a better understanding of the situation.

We will rst review the historical development of the theory, which started in the rst part of the 19th century in parallel with the development of the theory related to values of the exponential function.

Next we will deal with. We survey transcendence theory of values of elliptic functions in Section 3, linear independence in Section 4, and algebraic independence in Section 5. This splitting is somewhat artificial but convenient.

Moreover, we restrict ourselves to elliptic functions, even when many results are only special cases of statements valid for abelian functions. A transcendence measure -- Vanishing of linear forms without complex multiplication -- Vanishing of linear forms with complex multiplication -- An effective proof of a theorem of Coates -- A lower bound for non-vanishing linear forms -- Lemmas on elliptic functions with complex multiplication -- Linear forms in algebraic points.

If the address matches an existing account you will receive an email with instructions to reset your password. For further accounts of these types of results and their history, I highly recommend Waldschmidt's articles "Transcendence of periods: the state of the art," Pure Appl.

Math. 2 (), no. 2, part 2,and "Elliptic functions and transcendence," Surveys in number theory, Dev. Math. 17. Waldschmidt, Elliptic Functions and Transcendence (free) Books on Elliptic, Functions. Armitage, Eberlein, Elliptic Functions (unfree) Baker, Elliptic Functions, An Elementary Text-Book for Students of Mathematics (unfree) Bergman, Schiffer, Kernel Functions and Elliptic Differential Equations in Mathematical Physics (unfree).

Online shopping from a great selection at Books Store. Elliptic Curves, Modular Forms, and Their L-functions (Student Mathematical Library).

Four Lectures on Weierstrass Elliptic Function and Applications in Classical and Quantum Mechanics Georgios Pastras1 1NCSR \Demokritos", Institute of Nuclear and Particle Physics Aghia Paraskevi, Attiki, Greece [email protected] Abstract In these four lectures, aiming at senior undergraduate and junior graduate Physics.

Sep 28,  · In its first six chapters this text seeks to present the basic ideas and properties of the Jacobi elliptic functions as an historical essay, an attempt to answer the fascinating question: 'what would the treatment of elliptic functions have been like if Abel had developed the ideas, rather than Jacobi?' Accordingly, it is based on the idea of inverting integrals which arise in the theory 3/5(2).

Transcendence theory, advances and applications: proceedings of a conference held in Cambridge in From inside the book. What people are saying - Write a review. We haven't found any reviews in the usual places. Contents. Applications of the GelfondBaker Method to Dio Congresses Elliptic functions Elliptic functions - Congresses.

Cambridge Core - Number Theory - Elliptic Functions - by J. Armitage. In its first six chapters this text seeks to present the basic ideas and properties of the Jacobi elliptic functions as an historical essay, an attempt to answer the fascinating question: 'what would the treatment of elliptic functions have been like if Abel had developed the ideas, rather than Jacobi?'Cited by: 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 Weierstrass’s Elliptic Function.

Pages. May 04,  · Read "Periods and Special Functions in Transcendence" by Paula Tretkoff available from Rakuten Kobo. This book gives an introduction to some central results in transcendental number theory with application to periods and.Condition: Neu.

This item is printed on demand - Print on Demand Neuware - An introduction in the theory of elliptic functions and elliptic curves. Both are a priori different mathematical subjects. However, there is a fascinating connection between elliptic curves and elliptic functions, which is a great example to show the beautiness of.Riemann zeta function as well as Hecke’s generalization of this to Dirichlet’s L-functions and derive an elliptic analogue.

We also discuss transcendence questions that arise from this analogue. Keywords Elliptic functions · Special values · Dirichlet’s L-series · Hurwitz zeta function · Eisenstein series · Transcendence.