Elliptic Functions According To Eisenstein And Kronecker

Author : Andre Weil
Publisher : Springer Science & Business Media
Page : 112 pages
File Size : 48,6 Mb
Release : 1999
Category : Mathematics
ISBN : 3540650369

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Elliptic Functions According to Eisenstein and Kronecker by Andre Weil Pdf

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 (...).

Author : André Weil
Publisher : Unknown
Page : 92 pages
File Size : 43,9 Mb
Release : 1999
Category : Elliptic functions
ISBN : 7510004667

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Elliptic Functions According to Eisenstein and Kronecker by André Weil Pdf

Author : Viktor Vasil_evich Prasolov,I_Uri_ Pavlovich Solov_ev
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 51,7 Mb
Release : 1997-09-16
Category : Mathematics
ISBN : 0821897802

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Elliptic Functions and Elliptic Integrals by Viktor Vasil_evich Prasolov,I_Uri_ Pavlovich Solov_ev Pdf

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.

Author : Shaun Cooper
Publisher : World Scientific
Page : 185 pages
File Size : 42,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814366465

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Development of Elliptic Functions According to Ramanujan by Shaun Cooper Pdf

This unique book provides an innovative and efficient approach to elliptic functions, based on the ideas of the great Indian mathematician Srinivasa Ramanujan. The original 1988 monograph of K Venkatachaliengar has been completely revised. Many details, omitted from the original version, have been included, and the book has been made comprehensive by notes at the end of each chapter. The book is for graduate students and researchers in Number Theory and Classical Analysis, as well for scholars and aficionados of Ramanujan''s work. It can be read by anyone with some undergraduate knowledge of real and complex analysis.

Author : Komaravolu Chandrasekharan
Publisher : Springer Science & Business Media
Page : 199 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642522444

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Elliptic Functions by Komaravolu Chandrasekharan Pdf

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.

Author : Andrei N. Kolmogorov,Adolf-Andrei P. Yushkevich
Publisher : Birkhäuser
Page : 300 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034891738

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Mathematics of the 19th Century by Andrei N. Kolmogorov,Adolf-Andrei P. Yushkevich Pdf

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).

Author : Ranjan Roy
Publisher : Cambridge University Press
Page : 491 pages
File Size : 46,9 Mb
Release : 2017-04-18
Category : Mathematics
ISBN : 9781107159389

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Elliptic and Modular Functions from Gauss to Dedekind to Hecke by Ranjan Roy Pdf

A thorough guide to elliptic functions and modular forms that demonstrates the relevance and usefulness of historical sources.

Author : Heinrich Begehr,Helmut Koch,Jürg Kramer,Norbert Schappacher,Ernst-Jochen Thiele
Publisher : Birkhäuser
Page : 204 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034887878

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Mathematics in Berlin by Heinrich Begehr,Helmut Koch,Jürg Kramer,Norbert Schappacher,Ernst-Jochen Thiele Pdf

This little book is conceived as a service to mathematicians attending the 1998 International Congress of Mathematicians in Berlin. It presents a comprehensive, condensed overview of mathematical activity in Berlin, from Leibniz almost to the present day (without, however, including biographies of living mathematicians). Since many towering figures in mathematical history worked in Berlin, most of the chapters of this book are concise biographies. These are held together by a few survey articles presenting the overall development of entire periods of scientific life at Berlin. Overlaps between various chapters and differences in style between the chap ters were inevitable, but sometimes this provided opportunities to show different aspects of a single historical event - for instance, the Kronecker-Weierstrass con troversy. The book aims at readability rather than scholarly completeness. There are no footnotes, only references to the individual bibliographies of each chapter. Still, we do hope that the texts brought together here, and written by the various authors for this volume, constitute a solid introduction to the history of Berlin mathematics.

Author : J. V. Armitage,W. F. Eberlein
Publisher : Cambridge University Press
Page : 9 pages
File Size : 46,6 Mb
Release : 2006-09-28
Category : Mathematics
ISBN : 9781139457491

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Elliptic Functions by J. V. Armitage,W. F. Eberlein Pdf

In its first six chapters this 2006 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 of differential equations and, in particular, the differential equation that describes the motion of a simple pendulum. The later chapters present a more conventional approach to the Weierstrass functions and to elliptic integrals, and then the reader is introduced to the richly varied applications of the elliptic and related functions. Applications spanning arithmetic (solution of the general quintic, the functional equation of the Riemann zeta function), dynamics (orbits, Euler's equations, Green's functions), and also probability and statistics, are discussed.

Author : Johannes Blümlein,Carsten Schneider,Peter Paule
Publisher : Springer
Page : 509 pages
File Size : 44,8 Mb
Release : 2019-01-30
Category : Computers
ISBN : 9783030044800

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Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory by Johannes Blümlein,Carsten Schneider,Peter Paule Pdf

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.

Author : Serge G. Vlăduț
Publisher : CRC Press
Page : 426 pages
File Size : 43,8 Mb
Release : 1991
Category : Mathematics
ISBN : 2881247547

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Kronecker's Jugendtraum and Modular Functions by Serge G. Vlăduț Pdf

During the second half of the 19th century, Leopold Kronecker cherished a dream, his Jugendtraum, that he should see the formulation of a complete theory of complex multiplication. Kronecker's papers devoted to his Jugendtraum constitute the foundations of the arithmetical theory of modular functions. Vladut has studied the dream, and traces the development of elliptic function theory from its genesis to its most recent achievements. Included is a reprint of Kronecker's 1886 paper which presents many of the principal ideas of the arithmetical theory of modular functions. Translated from the Russian. Annotation copyrighted by Book News, Inc., Portland, OR

Author : Mathieu Marion
Publisher : OUP Oxford
Page : 272 pages
File Size : 40,5 Mb
Release : 1998-12-17
Category : Philosophy
ISBN : 9780191568329

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Wittgenstein, Finitism, and the Foundations of Mathematics by Mathieu Marion Pdf

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.

Author : Mathieu Marion,Robert S. Cohen
Publisher : Springer Science & Business Media
Page : 476 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400915756

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Québec Studies in the Philosophy of Science by Mathieu Marion,Robert S. Cohen Pdf

By North-American standards, philosophy is not new in Quebec: the first men tion of philosophy lectures given by a Jesuit in the College de Quebec (founded 1635) dates from 1665, and the oldest logic manuscript dates from 1679. In English-speaking universities such as McGill (founded 1829), philosophy began to be taught later, during the second half of the 19th century. The major influence on English-speaking philosophers was, at least initially, that of Scottish Empiricism. On the other hand, the strong influence of the Catholic Church on French-Canadian society meant that the staff of the facultes of the French-speaking universities consisted, until recently, almost entirely of Thomist philosophers. There was accordingly little or no work in modem Formal Logic and Philosophy of Science and precious few contacts between the philosophical communities. In the late forties, Hugues Leblanc was a young student wanting to learn Formal Logic. He could not find anyone in Quebec to teach him and he went to study at Harvard University under the supervision of W. V. Quine. His best friend Maurice L' Abbe had left, a year earlier, for Princeton to study with Alonzo Church. After receiving his Ph. D from Harvard in 1948, Leblanc started his profes sional career at Bryn Mawr College, where he stayed until 1967. He then went to Temple University, where he taught until his retirement in 1992, serving as Chair of the Department of Philosophy from 1973 until 1979.

Author : M. Rapoport,P. Schneider,N. Schappacher
Publisher : Academic Press
Page : 399 pages
File Size : 53,8 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9781483263304

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Beilinson's Conjectures on Special Values of L-Functions by M. Rapoport,P. Schneider,N. Schappacher Pdf

Beilinson's Conjectures on Special Values of L-Functions deals with Alexander Beilinson's conjectures on special values of L-functions. Topics covered range from Pierre Deligne's conjecture on critical values of L-functions to the Deligne-Beilinson cohomology, along with the Beilinson conjecture for algebraic number fields and Riemann-Roch theorem. Beilinson's regulators are also compared with those of Émile Borel. Comprised of 10 chapters, this volume begins with an introduction to the Beilinson conjectures and the theory of Chern classes from higher k-theory. The "simplest" example of an L-function is presented, the Riemann zeta function. The discussion then turns to Deligne's conjecture on critical values of L-functions and its connection to Beilinson's version. Subsequent chapters focus on the Deligne-Beilinson cohomology; ?-rings and Adams operations in algebraic k-theory; Beilinson conjectures for elliptic curves with complex multiplication; and Beilinson's theorem on modular curves. The book concludes by reviewing the definition and properties of Deligne homology, as well as Hodge-D-conjecture. This monograph should be of considerable interest to researchers and graduate students who want to gain a better understanding of Beilinson's conjectures on special values of L-functions.

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 540 pages
File Size : 55,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9789400959880

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Encyclopaedia of Mathematics by Michiel Hazewinkel Pdf

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.