Introduction To Algebraic And Abelian Functions
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Author |
: Serge Lang |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 178 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781461257400 |
ISBN-13 |
: 1461257409 |
Rating |
: 4/5 (00 Downloads) |
Synopsis Introduction to Algebraic and Abelian Functions by : Serge Lang
Introduction to Algebraic and Abelian Functions is a self-contained presentation of a fundamental subject in algebraic geometry and number theory. For this revised edition, the material on theta functions has been expanded, and the example of the Fermat curves is carried throughout the text. This volume is geared toward a second-year graduate course, but it leads naturally to the study of more advanced books listed in the bibliography.
Author |
: Alekse_ Ivanovich Markushevich |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 188 |
Release |
: 2006-07-26 |
ISBN-10 |
: 0821898361 |
ISBN-13 |
: 9780821898369 |
Rating |
: 4/5 (61 Downloads) |
Synopsis Introduction to the Classical Theory of Abelian Functions by : Alekse_ Ivanovich Markushevich
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
Author |
: Serge Lang |
Publisher |
: |
Total Pages |
: 169 |
Release |
: 1982 |
ISBN-10 |
: OCLC:640090383 |
ISBN-13 |
: |
Rating |
: 4/5 (83 Downloads) |
Synopsis Introduction to Algebraic and Abelian Functions.-- 2nd Ed by : Serge Lang
Author |
: |
Publisher |
: |
Total Pages |
: 175 |
Release |
: 1962 |
ISBN-10 |
: 082184542X |
ISBN-13 |
: 9780821845424 |
Rating |
: 4/5 (2X Downloads) |
Synopsis Translations of Mathematical Monographs by :
Author |
: Kenkichi Iwasawa |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 314 |
Release |
: 1993 |
ISBN-10 |
: 9780821819692 |
ISBN-13 |
: 0821819690 |
Rating |
: 4/5 (92 Downloads) |
Synopsis Algebraic Functions by : Kenkichi Iwasawa
This is a translation of Iwasawa's 1973 book, Theory of Algebraic Functions originally published in Japanese. Because the book treats mainly the classical part of the theory of algebraic functions, emphasizing analytic methods, it provides an excellent introduction to the subject from the classical viewpoint. Directed at graduate students, the book requires some basic knowledge of algebra, topology, and functions of a complex variable.
Author |
: Henry Frederick Baker |
Publisher |
: Cambridge University Press |
Total Pages |
: 724 |
Release |
: 1995-12-14 |
ISBN-10 |
: 0521498775 |
ISBN-13 |
: 9780521498777 |
Rating |
: 4/5 (75 Downloads) |
Synopsis Abelian Functions by : Henry Frederick Baker
Classical algebraic geometry, inseparably connected with the names of Abel, Riemann, Weierstrass, Poincaré, Clebsch, Jacobi and other outstanding mathematicians of the last century, was mainly an analytical theory. In our century it has been enriched by the methods and ideas of topology, commutative algebra and Grothendieck's schemes seemed to have replaced once and forever the somewhat naive language of classical algebraic geometry. This book contains more than its modest title suggests. Written in 1897, its scope was as broad as it could possibly be, namely to cover the whole of algebraic geometry, and associated theories. The subject is discussed by Baker in terms of transcendental functions, and in particular theta functions. Many of the ideas put forward are of continuing relevance today, and some of the most exciting ideas from theoretical physics draw on work presented here.
Author |
: Vijaya Kumar Murty |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 128 |
Release |
: 1993 |
ISBN-10 |
: 9780821811795 |
ISBN-13 |
: 0821811797 |
Rating |
: 4/5 (95 Downloads) |
Synopsis Introduction to Abelian Varieties by : Vijaya Kumar Murty
This book presents an elementary and self-contained approach to Abelian varieties, a subject that plays a central role in algebraic and analytic geometry, number theory, and complex analysis. The book is based on notes from a course given at Concordia University and would be useful for independent study or as a textbook for graduate courses in complex analysis, Riemann surfaces, number theory, or analytic geometry. Murty works mostly over the complex numbers, discussing the theorem of Abel-Jacobi and Lefschetz's theorem on projective embeddings. After presenting some examples, Murty touches on Abelian varieties over number fields, as well as the conjecture of Tate (Faltings's theorem) and its relation to Mordell's conjecture. References are provided to guide the reader in further study.
Author |
: P.M. Cohn |
Publisher |
: CRC Press |
Total Pages |
: 204 |
Release |
: 2018-01-18 |
ISBN-10 |
: 9781351078030 |
ISBN-13 |
: 1351078038 |
Rating |
: 4/5 (30 Downloads) |
Synopsis Algebraic Numbers and Algebraic Functions by : P.M. Cohn
This book is an introduction to the theory of algebraic numbers and algebraic functions of one variable. The basic development is the same for both using E Artin's legant approach, via valuations. Number Theory is pursued as far as the unit theorem and the finiteness of the class number. In function theory the aim is the Abel-Jacobi theorem describing the devisor class group, with occasional geometrical asides to help understanding. Assuming only an undergraduate course in algebra, plus a little acquaintance with topology and complex function theory, the book serves as an introduction to more technical works in algebraic number theory, function theory or algebraic geometry by an exposition of the central themes in the subject.
Author |
: George R. Kempf |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 108 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783642760792 |
ISBN-13 |
: 3642760791 |
Rating |
: 4/5 (92 Downloads) |
Synopsis Complex Abelian Varieties and Theta Functions by : George R. Kempf
Abelian varieties are a natural generalization of elliptic curves to higher dimensions, whose geometry and classification are as rich in elegant results as in the one-dimensional ease. The use of theta functions, particularly since Mumford's work, has been an important tool in the study of abelian varieties and invertible sheaves on them. Also, abelian varieties play a significant role in the geometric approach to modern algebraic number theory. In this book, Kempf has focused on the analytic aspects of the geometry of abelian varieties, rather than taking the alternative algebraic or arithmetic points of view. His purpose is to provide an introduction to complex analytic geometry. Thus, he uses Hermitian geometry as much as possible. One distinguishing feature of Kempf's presentation is the systematic use of Mumford's theta group. This allows him to give precise results about the projective ideal of an abelian variety. In its detailed discussion of the cohomology of invertible sheaves, the book incorporates material previously found only in research articles. Also, several examples where abelian varieties arise in various branches of geometry are given as a conclusion of the book.
Author |
: Goro Shimura |
Publisher |
: Princeton University Press |
Total Pages |
: 232 |
Release |
: 2016-06-02 |
ISBN-10 |
: 9781400883943 |
ISBN-13 |
: 1400883946 |
Rating |
: 4/5 (43 Downloads) |
Synopsis Abelian Varieties with Complex Multiplication and Modular Functions by : Goro Shimura
Reciprocity laws of various kinds play a central role in number theory. In the easiest case, one obtains a transparent formulation by means of roots of unity, which are special values of exponential functions. A similar theory can be developed for special values of elliptic or elliptic modular functions, and is called complex multiplication of such functions. In 1900 Hilbert proposed the generalization of these as the twelfth of his famous problems. In this book, Goro Shimura provides the most comprehensive generalizations of this type by stating several reciprocity laws in terms of abelian varieties, theta functions, and modular functions of several variables, including Siegel modular functions. This subject is closely connected with the zeta function of an abelian variety, which is also covered as a main theme in the book. The third topic explored by Shimura is the various algebraic relations among the periods of abelian integrals. The investigation of such algebraicity is relatively new, but has attracted the interest of increasingly many researchers. Many of the topics discussed in this book have not been covered before. In particular, this is the first book in which the topics of various algebraic relations among the periods of abelian integrals, as well as the special values of theta and Siegel modular functions, are treated extensively.