Introduction To The Classical Theory Of Abelian Functions

Author : Alekse_ Ivanovich Markushevich
Publisher : American Mathematical Soc.
Page : 188 pages
File Size : 46,6 Mb
Release : 2006-07-26
Category : Mathematics
ISBN : 0821898361

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Introduction to the Classical Theory of Abelian Functions by Alekse_ Ivanovich Markushevich Pdf

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 : Anonim
Publisher : Unknown
Page : 175 pages
File Size : 52,6 Mb
Release : 1962
Category : Functions, Abelian
ISBN : 082184542X

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Translations of Mathematical Monographs by Anonim Pdf

Author : Henry Frederick Baker
Publisher : Cambridge University Press
Page : 724 pages
File Size : 40,7 Mb
Release : 1995-12-14
Category : Mathematics
ISBN : 0521498775

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Abelian Functions by Henry Frederick Baker Pdf

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 : Kenkichi Iwasawa
Publisher : American Mathematical Soc.
Page : 314 pages
File Size : 47,6 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821819692

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Algebraic Functions by Kenkichi Iwasawa Pdf

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 : Unknown
Page : 360 pages
File Size : 48,9 Mb
Release : 1907
Category : Functions
ISBN : STANFORD:36105033017620

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An Introduction to the Theory of Multiply Periodic Functions by Henry Frederick Baker Pdf

Author : Guan-hou Zhang
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 51,6 Mb
Release : 1993-01-01
Category : Mathematics
ISBN : 0821887645

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Theory of Entire and Meromorphic Functions by Guan-hou Zhang Pdf

This book was originally written in Chinese in 1986 by the noted complex analyst Zhang Guan-Hou, who was a research fellow at the Academia Sinica. The book provides a basic introduction to the development of the theory of entire and meromorphic functions from the 1950s to the early 1980s. After an opening chapter introducing fundamentals of Nevanlinna's value distribution theory, this book discusses various relationships among and developments of three central concepts: deficient value, asymptotic value, and singular direction. This book describes many significant results and research directions developed by Zhang and other Chinese complex analysts and published in Chinese mathematical journals. A comprehensive and self-contained reference, this book is useful for graduate students and researchers in complex analysis.

Author : Gennadiĭ Mikhaĭlovich Goluzin
Publisher : American Mathematical Soc.
Page : 690 pages
File Size : 46,9 Mb
Release : 1969
Category : Functions of complex variables
ISBN : 082188655X

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Geometric Theory of Functions of a Complex Variable by Gennadiĭ Mikhaĭlovich Goluzin Pdf

Author : Viktor Prasolov,Yuri Solovyev
Publisher : American Mathematical Society
Page : 198 pages
File Size : 54,7 Mb
Release : 1997-09-16
Category : Mathematics
ISBN : 9780821813461

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Elliptic Functions and Elliptic Integrals by Viktor Prasolov,Yuri Solovyev 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 : Mark Lʹvovich Agranovskiĭ
Publisher : American Mathematical Soc.
Page : 158 pages
File Size : 46,9 Mb
Release : 1993-01-01
Category : Mathematics
ISBN : 0821897470

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Invariant Function Spaces on Homogeneous Manifolds of Lie Groups and Applications by Mark Lʹvovich Agranovskiĭ Pdf

This book studies translation-invariant function spaces and algebras on homogeneous manifolds. The central topic is the relationship between the homogeneous structure of a manifold and the class of translation-invariant function spaces and algebras on the manifold. The author obtains classifications of translation-invariant spaces and algebras of functions on semisimple and nilpotent Lie groups, Riemann symmetric spaces, and bounded symmetric domains. When such classifications are possible, they lead in many cases to new characterizations of the classical function spaces, from the point of view of their group of admissible changes of variable. The algebra of holomorphic functions plays an essential role in these classifications when a homogeneous complex or $CR$-structure exists on the manifold. This leads to new characterizations of holomorphic functions and their boundary values for one- and multidimensional complex domains.

Author : Vijaya Kumar Murty
Publisher : American Mathematical Soc.
Page : 128 pages
File Size : 43,6 Mb
Release : 1993
Category : Abelian varieties
ISBN : 9780821811795

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Introduction to Abelian Varieties by Vijaya Kumar Murty Pdf

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 : Masaru Takeuchi
Publisher : American Mathematical Soc.
Page : 286 pages
File Size : 45,7 Mb
Release : 1994
Category : Spherical functions
ISBN : 0821845802

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Modern Spherical Functions by Masaru Takeuchi Pdf

This book presents an exposition of spherical functions on compact symmetric spaces, from the viewpoint of Cartan-Selberg. Representation theory, invariant differential operators, and invariant integral operators play an important role in the exposition. The author treats compact symmetric pairs, spherical representations for compact symmetric pairs, the fundamental groups of compact symmetric spaces, and the radial part of an invariant differential operator. Also explored are the classical results for spheres and complex projective spaces and the relation between spherical functions and harmonic polynomials. This book is suitable as a graduate textbook.

Author : Henry F. Baker
Publisher : Unknown
Page : 684 pages
File Size : 42,6 Mb
Release : 1995
Category : Electronic
ISBN : OCLC:1071734843

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Abelian functions by Henry F. Baker Pdf

Author : Vladimir Vasilʹevich Sharko
Publisher : American Mathematical Soc.
Page : 210 pages
File Size : 40,7 Mb
Release : 1993
Category : Mathematics
ISBN : 0821845780

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Functions on Manifolds: Algebraic and Topological Aspects by Vladimir Vasilʹevich Sharko Pdf

This monograph covers in a unified manner new results on smooth functions on manifolds. A major topic is Morse and Bott functions with a minimal number of singularities on manifolds of dimension greater than five. Sharko computes obstructions to deformation of one Morse function into another on a simply connected manifold. In addition, a method is developed for constructing minimal chain complexes and homotopical systems in the sense of Whitehead. This leads to conditions under which Morse functions on non-simply-connected manifolds exist. Sharko also describes new homotopical invariants of manifolds, which are used to substantially improve the Morse inequalities. The conditions guaranteeing the existence of minimal round Morse functions are discussed.

Author : Gennadiĭ Mikhaĭlovich Felʹdman
Publisher : American Mathematical Soc.
Page : 236 pages
File Size : 41,9 Mb
Release : 1993
Category : Mathematics
ISBN : 0821845934

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Arithmetic of Probability Distributions, and Characterization Problems on Abelian Groups by Gennadiĭ Mikhaĭlovich Felʹdman Pdf

This book studies the problem of the decomposition of a given random variable introduction a sum of independent random variables (components). The central feature of the book is Feldman's use of powerful analytical techniques.

Author : Gennadij M. Fel'dman
Publisher : American Mathematical Soc.
Page : 236 pages
File Size : 51,8 Mb
Release : 2024-07-02
Category : Mathematics
ISBN : 0821897446

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Arithmetic of Probability Distributions, and Characterization Problems on Abelian Groups by Gennadij M. Fel'dman Pdf

This book studies the problem of the decomposition of a given random variable introduction a sum of independent random variables (components). The central feature of the book is Feldman's use of powerful analytical techniques.