Elliptic Functions According To Eisenstein And Kronecker
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Elliptic Functions According To Eisenstein And Kronecker
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Author : Andre Weil
language : en
Publisher: Springer Science & Business Media
Release Date : 1999
Elliptic Functions According To Eisenstein And Kronecker written by Andre Weil 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 1999 with Mathematics categories.
Drawn from the Foreword: (...) On the other hand, since much of the material in this volume seems suitable for inclusion in elementary courses, it may not be superfluous to point out that it is almost entirely self-contained. Even the basic facts about trigonometric functions are treated ab initio in Ch. II, according to Eisenstein's method. It would have been both logical and convenient to treat the gamma -function similarly in Ch. VII; for the sake of brevity, this has not been done, and a knowledge of some elementary properties of T(s) has been assumed. One further prerequisite in Part II is Dirichlet's theorem on Fourier series, together with the method of Poisson summation which is only a special case of that theorem; in the case under consideration (essentially no more than the transformation formula for the theta-function) this presupposes the calculation of some classical integrals. (...) As to the final chapter, it concerns applications to number theory (...).
Elliptic Functions According To Eisenstein And Kronecker
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Author : André Weil
language : en
Publisher:
Release Date : 1999
Elliptic Functions According To Eisenstein And Kronecker written by André Weil and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Elliptic functions categories.
Elliptic Functions And Modular Forms
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Author : Max Koecher
language : en
Publisher: Springer Nature
Release Date : 2025-04-30
Elliptic Functions And Modular Forms written by Max Koecher and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-30 with Mathematics categories.
The theory of elliptic functions and modular forms is rich and storied, though it has a reputation for difficulty. In this textbook, the authors successfully bridge foundational concepts and advanced material. Following Weierstrass’s approach to elliptic functions, they also cover elliptic curves and complex multiplication. The sections on modular forms, which can be read independently, include discussions of Hecke operators and Dirichlet series. Special emphasis is placed on theta series, with some advanced results included. With detailed proofs and numerous exercises, this book is well-suited for self-study or use as a reference. A companion website provides videos and a discussion forum on the topic.
Elliptic Integrals Elliptic Functions And Modular Forms In Quantum Field Theory
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Author : Johannes Blümlein
language : en
Publisher: Springer
Release Date : 2019-01-30
Elliptic Integrals Elliptic Functions And Modular Forms In Quantum Field Theory written by Johannes Blümlein and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-30 with Computers categories.
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.
Elliptic Functions
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Author : Komaravolu Chandrasekharan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Elliptic Functions written by Komaravolu Chandrasekharan 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.
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.
Elliptic And Modular Functions From Gauss To Dedekind To Hecke
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Author : Ranjan Roy
language : en
Publisher: Cambridge University Press
Release Date : 2017-04-18
Elliptic And Modular Functions From Gauss To Dedekind To Hecke written by Ranjan Roy 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 2017-04-18 with Mathematics categories.
A thorough guide to elliptic functions and modular forms that demonstrates the relevance and usefulness of historical sources.
Mathematics Of The 19th Century
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Author : Andrei N. Kolmogorov
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Mathematics Of The 19th Century written by Andrei N. Kolmogorov and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The general principles by which the editors and authors of the present edition have been guided were explained in the preface to the first volume of Mathemat ics of the 19th Century, which contains chapters on the history of mathematical logic, algebra, number theory, and probability theory (Nauka, Moscow 1978; En glish translation by Birkhiiuser Verlag, Basel-Boston-Berlin 1992). Circumstances beyond the control of the editors necessitated certain changes in the sequence of historical exposition of individual disciplines. The second volume contains two chapters: history of geometry and history of analytic function theory (including elliptic and Abelian functions); the size of the two chapters naturally entailed di viding them into sections. The history of differential and integral calculus, as well as computational mathematics, which we had planned to include in the second volume, will form part of the third volume. We remind our readers that the appendix of each volume contains a list of the most important literature and an index of names. The names of journals are given in abbreviated form and the volume and year of publication are indicated; if the actual year of publication differs from the nominal year, the latter is given in parentheses. The book History of Mathematics from Ancient Times to the Early Nineteenth Century [in Russian], which was published in the years 1970-1972, is cited in abbreviated form as HM (with volume and page number indicated). The first volume of the present series is cited as Bk. 1 (with page numbers).
Galois Representations In Arithmetic Algebraic Geometry
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Author : A. J. Scholl
language : en
Publisher: Cambridge University Press
Release Date : 1998-11-26
Galois Representations In Arithmetic Algebraic Geometry written by A. J. Scholl 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 1998-11-26 with Mathematics categories.
Conference proceedings based on the 1996 LMS Durham Symposium 'Galois representations in arithmetic algebraic geometry'.
Introduction To The Classical Theory Of Abelian Functions
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Author : Alekse_ Ivanovich Markushevich
language : en
Publisher: American Mathematical Soc.
Release Date : 2006-07-26
Introduction To The Classical Theory Of Abelian Functions written by Alekse_ Ivanovich Markushevich 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 2006-07-26 with Mathematics categories.
Historical introduction. The Jacobian inversion problem Periodic functions of several complex variables Riemann matrices. Jacobian (intermediate) functions Construction of Jacobian functions of a given type. Theta functions and Abelian functions. Abelian and Picard manifolds Appendix A. Skew-symmetric determinants Appendix B. Divisors of analytic functions Appendix C. A summary of the most important formulas
Wittgenstein Finitism And The Foundations Of Mathematics
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Author : Mathieu Marion
language : en
Publisher: OUP Oxford
Release Date : 1998-12-17
Wittgenstein Finitism And The Foundations Of Mathematics written by Mathieu Marion and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-12-17 with Philosophy categories.
Mathieu Marion offers a careful, historically informed study of Wittgenstein's philosophy of mathematics. This area of his work has frequently been undervalued by Wittgenstein specialists and by philosophers of mathematics alike; but the surprising fact that he wrote more on this subject than on any other indicates its centrality in his thought. Marion traces the development of Wittgenstein's thinking in the context of the mathematical and philosophical work of the times, to make coherent sense of ideas that have too often been misunderstood because they have been presented in a disjointed and incomplete way. In particular, he illuminates the work of the neglected 'transitional period' between the Tractatus and the Investigations. Marion shows that study of Wittgenstein's writings on mathematics is essential to a proper understanding of his philosophy; and he also demonstrates that it has much to contribute to current debates about the foundations of mathematics.