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Automorphic Functions


Automorphic Functions
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Introduction To The Arithmetic Theory Of Automorphic Functions


Introduction To The Arithmetic Theory Of Automorphic Functions
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Author : Gorō Shimura
language : en
Publisher: Princeton University Press
Release Date : 1971-08-21

Introduction To The Arithmetic Theory Of Automorphic Functions written by Gorō Shimura and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971-08-21 with Mathematics categories.


The theory of automorphic forms is playing increasingly important roles in several branches of mathematics, even in physics, and is almost ubiquitous in number theory. This book introduces the reader to the subject and in particular to elliptic modular forms with emphasis on their number-theoretical aspects. After two chapters geared toward elementary levels, there follows a detailed treatment of the theory of Hecke operators, which associate zeta functions to modular forms. At a more advanced level, complex multiplication of elliptic curves and abelian varieties is discussed. The main question is the construction of abelian extensions of certain algebraic number fields, which is traditionally called "Hilbert's twelfth problem." Another advanced topic is the determination of the zeta function of an algebraic curve uniformized by modular functions, which supplies an indispensable background for the recent proof of Fermat's last theorem by Wiles.



Automorphic Functions


Automorphic Functions
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Author : Lester R. Ford
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

Automorphic Functions written by Lester R. Ford 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 2004 with Mathematics categories.


Lester Ford's book was the first treatise in English on automorphic functions. At the time of its publication (1929), it was welcomed for its elegant treatment of groups of linear transformations and for the remarkably clear and explicit exposition throughout the book. Ford's extraordinary talent for writing has been memorialized in the prestigious award that bears his name. The book, in the meantime, has become a recognized classic. Ford's approach is primarily through analytic function theory. The first part of the book covers groups of linear transformations, especially Fuchsian groups, fundamental domains, and functions that are invariant under the groups, including the classical elliptic modular functions and Poincare theta series. The second part of the book covers conformal mappings, uniformization, and connections between automorphic functions and differential equations with regular singular points, such as the hypergeometric equation.



Spectral Theory Of Automorphic Functions


Spectral Theory Of Automorphic Functions
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Author : A.B. Venkov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Spectral Theory Of Automorphic Functions written by A.B. Venkov 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.


'Et moi ..., si j'avait su comment en revcnrr, One service mathematics has rendered the je n'y serais point aile.' human race. It has put common sense back. Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.



Automorphic Functions And Number Theory


Automorphic Functions And Number Theory
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Author : Goro Shimura
language : en
Publisher: Springer
Release Date : 2006-11-15

Automorphic Functions And Number Theory written by Goro Shimura and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.




Introduction To The Arithmetic Theory Of Automorphic Functions


Introduction To The Arithmetic Theory Of Automorphic Functions
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Author : Gorō Shimura
language : en
Publisher: Princeton University Press
Release Date : 1971-08-21

Introduction To The Arithmetic Theory Of Automorphic Functions written by Gorō Shimura and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971-08-21 with Mathematics categories.


The theory of automorphic forms is playing increasingly important roles in several branches of mathematics, even in physics, and is almost ubiquitous in number theory. This book introduces the reader to the subject and in particular to elliptic modular forms with emphasis on their number-theoretical aspects. After two chapters geared toward elementary levels, there follows a detailed treatment of the theory of Hecke operators, which associate zeta functions to modular forms. At a more advanced level, complex multiplication of elliptic curves and abelian varieties is discussed. The main question is the construction of abelian extensions of certain algebraic number fields, which is traditionally called "Hilbert's twelfth problem." Another advanced topic is the determination of the zeta function of an algebraic curve uniformized by modular functions, which supplies an indispensable background for the recent proof of Fermat's last theorem by Wiles.



Discontinuous Groups And Automorphic Functions


Discontinuous Groups And Automorphic Functions
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Author : Joseph Lehner
language : en
Publisher: American Mathematical Soc.
Release Date : 1964-12-31

Discontinuous Groups And Automorphic Functions written by Joseph Lehner 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 1964-12-31 with Mathematics categories.


Much has been written on the theory of discontinuous groups and automorphic functions since 1880, when the subject received its first formulation. The purpose of this book is to bring together in one place both the classical and modern aspects of the theory, and to present them clearly and in a modern language and notation. The emphasis in this book is on the fundamental parts of the subject. The book is directed to three classes of readers: graduate students approaching the subject for the first time, mature mathematicians who wish to gain some knowledge and understanding of automorphic function theory, and experts.



An Introduction To The Theory Of Automorphic Functions


An Introduction To The Theory Of Automorphic Functions
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Author : Lester R. Ford
language : en
Publisher:
Release Date : 1915

An Introduction To The Theory Of Automorphic Functions written by Lester R. Ford and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1915 with Automorphic functions categories.




Almost Periodic And Almost Automorphic Functions In Abstract Spaces


Almost Periodic And Almost Automorphic Functions In Abstract Spaces
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Author : Gaston M. N'Guérékata
language : en
Publisher: Springer Nature
Release Date : 2021-05-28

Almost Periodic And Almost Automorphic Functions In Abstract Spaces written by Gaston M. N'Guérékata and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-28 with Mathematics categories.


This book presents the foundation of the theory of almost automorphic functions in abstract spaces and the theory of almost periodic functions in locally and non-locally convex spaces and their applications in differential equations. Since the publication of Almost automorphic and almost periodic functions in abstract spaces (Kluwer Academic/Plenum, 2001), there has been a surge of interest in the theory of almost automorphic functions and applications to evolution equations. Several generalizations have since been introduced in the literature, including the study of almost automorphic sequences, and the interplay between almost periodicity and almost automorphic has been exposed for the first time in light of operator theory, complex variable functions and harmonic analysis methods. As such, the time has come for a second edition to this work, which was one of the most cited books of the year 2001. This new edition clarifies and improves upon earlier materials, includes many relevant contributions and references in new and generalized concepts and methods, and answers the longtime open problem, "What is the number of almost automorphic functions that are not almost periodic in the sense of Bohr?" Open problems in non-locally convex valued almost periodic and almost automorphic functions are also indicated. As in the first edition, materials are presented in a simplified and rigorous way. Each chapter is concluded with bibliographical notes showing the original sources of the results and further reading.



Almost Automorphic And Almost Periodic Functions In Abstract Spaces


Almost Automorphic And Almost Periodic Functions In Abstract Spaces
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Author : Gaston M. N'Guérékata
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Almost Automorphic And Almost Periodic Functions In Abstract Spaces written by Gaston M. N'Guérékata 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 2013-04-17 with Mathematics categories.


Almost Automorphic and Almost Periodic Functions in Abstract Spaces introduces and develops the theory of almost automorphic vector-valued functions in Bochner's sense and the study of almost periodic functions in a locally convex space in a homogenous and unified manner. It also applies the results obtained to study almost automorphic solutions of abstract differential equations, expanding the core topics with a plethora of groundbreaking new results and applications. For the sake of clarity, and to spare the reader unnecessary technical hurdles, the concepts are studied using classical methods of functional analysis.



Discrete Groups And Automorphic Functions


Discrete Groups And Automorphic Functions
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Author : W. J. Harvey (Ph. D.)
language : en
Publisher:
Release Date : 1977

Discrete Groups And Automorphic Functions written by W. J. Harvey (Ph. D.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Mathematics categories.