Last edited by Yozuru
Tuesday, May 5, 2020 | History

2 edition of Discontinuous groups and automorphic functions found in the catalog.

Discontinuous groups and automorphic functions

Joseph Lehner

# Discontinuous groups and automorphic functions

## by Joseph Lehner

Written in English

Subjects:
• Functions, Automorphic.,
• Discontinuous groups.

• Edition Notes

Includes bibliography, p. 409-418 and index.

Classifications The Physical Object Statement Joseph Lehner. Series Mathematical surveys -- no.8 LC Classifications QA351 Pagination xi, 425 p. : Number of Pages 425 Open Library OL20351250M

In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group G to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup ⊂ of the topological group. Automorphic forms are a generalization of the idea of periodic functions in Euclidean space to general topological groups. Discontinuous Groups and Automorphic Functions, Math. Surveys No. 8, Amer. Math. Soc. [Classical and careful, detailed treatment of subgroups of modular groups] (5) Toshitsune Miyake, Modular Forms, Springer-Verlag (6) H. Maass, Lectures on Modular Functions of One Complex Variable Tata Institute Lecture Notes: Bombay (revised ).

This book, which is volume 17 in the AMS/LMS history series, contains a small book by Jacques Hadamard on the connections between non-Euclidean geometry and the theory of automorphic functions. Hadamard's book was written in the s for publication in Russia, appearing in a series entitled "The Geometry of Lobachevskii and the Development of. Author Joseph Lehner begins by elaborating on the theory of discontinuous groups by the classical method of Poincaré, employing the model of the hyperbolic plane. The necessary hyperbolic geometry is developed in the text. Chapter two develops automorphic functions and forms via the Poincaré : Joseph Lehner.

Abstract. This paper contains the Bass-Serre theory generalizing free products with amalgamation and HNNextensions; the structure of finite extensions of free groups and applications to finite group actions on surfaces; and the theory of planar discontinuous by: 9. Carl L. Siegel () was one of the finest mathematicians of the twentieth century. The present book is a set of lectures on favorite themes of Siegel, delivered at the Institute for Advanced Study in The notes on which the book was based were drawn up with great care by Paul T. Bateman.

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### Discontinuous groups and automorphic functions by Joseph Lehner Download PDF EPUB FB2

Much has been written on the theory of discontinuous groups and automorphic functions sincewhen 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 by: Much has been written on the theory of discontinuous groups and automorphic functions sincewhen the subject received its first formulation.

This book intends 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.

1 Discontinuous Groups 3 2 Geometry of Γ 7 4 Existence of Automorphic Functions on Fuchsian Groups 17 Beardon’s book [3] on discrete groups and Ford’s book [4] in which he introduced the isometric circle.

Acknowledgment is also due to Dr Kovalev and Dr Carne for their lecture courses on. This concise three-part treatment introduces undergraduate and graduate students to the theory of automorphic functions and discontinuous Discontinuous groups and automorphic functions book.

Author Joseph Lehner begins by elaborating on the theory of discontinuous groups by the classical method of Poincaré, employing the model of the hyperbolic by: COVID Resources.

Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle.

Much has been written on the theory of discontinuous groups and automorphic functions sincewhen 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.

Much has been written on the theory of discontinuous groups and automorphic functions sincewhen 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.

This nice little book was originally published in in the famous “Athena Series” of short mathematical monographs. It offers a very clear, if somewhat old-fashioned, introduction to the classical theory of discontinuous groups and automorphic functions. This concise three-part treatment introduces undergraduate and graduate students to the theory of automorphic functions and discontinuous groups.

The text begins with the basics of Fuchsian groups, advancing to the development of Poincaré series and automorphic forms and concluding with the connection between the theory of Riemann surfaces with theories of automorphic.

This book is an outgrowth of the twelfth Summer Mathematical Institute of the American Mathematical Society, which was devoted to Algebraic Groups and Discontinuous Subgroups. The Institute was held at the University of Colorado in Boulder from July S to August 6,and was financed by the National Science Foundation and the Office of Naval Research.

The. Lester Ford's book was the first treatise in English on automorphic functions. At the time of its publication (), 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.5/5(1).

In mathematics, an automorphic function is a function on a space that is invariant under the action of some group, in other words a function on the quotient the space is a complex manifold and the group is a discrete group. Examples. Kleinian group; Elliptic modular function; Modular function; References.

Andrianov, A.N.; Parshin, A.N. () [], "Automorphic. Condition: New. Paperback. This concise three-part treatment introduces undergraduate and graduate students to the theory of automorphic functions and discontinuous groups. The text begins with the basics of ng may be from multiple locations in the US or from the UK, depending on stock availability.

pages. AUTOMORPHIC FUNCTIONS OF SEVERAL COMPLEX VARIABLES 1. The Space U and its Analytic Mappings 2. Discontinuous Groups 3. Analytic Functions of n Complex Variables 4. The Fundamental Region 5. Poincare Series 6.

Automorphic Functions 7. The Field of Automorphic Functions Notes List of References Index This concise three-part treatment introduces undergraduate and graduate students to the theory of automorphic functions and discontinuous groups.

Author Joseph Lehner begins by elaborating on the theory of discontinuous groups by the classical method of Poincar, employing the model of the hyperbolic plane. Author Joseph Lehner begins by elaborating on the theory of discontinuous groups by the classical method of Poincaré, employing the model of the hyperbolic plane.

The necessary hyperbolic geometry is developed in the text. Chapter two develops automorphic functions and forms via the Poincaré series.

Discontinuous Groups and Automorphic Forms 11Fxx. Scott Ahlgren, On the irreducibility of Hecke polynomials, Math. Comp. 77 (), no.– Scott Ahlgren and Ken Ono, Arithmetic of singular moduli and class polynomials, Compos.

Math. (), no. 2, – Algebraic Groups and Discontinuous Subgroups by Armand Borel, George D. Mostow. Publisher: American Mathematical Society ISBN/ASIN: ISBN Number of pages: Description: The book is concentrated around five major themes: linear algebraic groups and arithmetic groups, adeles and arithmetic properties of algebraic groups.

This concise three-part treatment introduces undergraduate and graduate students to the theory of automorphic functions and discontinuous groups. Author Joseph Lehner begins by elaborating on the theory of discontinuous groups by the classical method of Poincaré, employing the model of the hyperbolic plane.

Chapter I Discontinuous Groups 1. 1 Linear Transformations 1. 2 Real Discontinuous Groups 3 The Limit set of a Discrete Group 4 The Fundamental Region 5 The Hyperbolic Area of the Fundamental Region 6 Examples Chapter II Automorphic Functions and Automorphic Forms 1 Existence 2 The Divisor of an Automorphic Author: Joseph Lehner.

Poincare's work in the theory of automorphic functions is a J Lehner, Discontinuous groups and automorphic junctions, American lViathematical Society, (This provides a The following book is the best source for the arithmetic as­.Symplectic Geometry focuses on the processes, methodologies, and numerical approaches involved in symplectic geometry.

The book first offers information on the symplectic and discontinuous groups, symplectic metric, and hermitian forms. Numerical calculations are presented to show the values and transformations of these groups.In the first case the discrete groups $\Gamma$ are finite, the curves $M / \Gamma$ are algebraic curves of genus 0 (cf.

Genus of a curve) and, consequently, the automorphic functions generate a field of rational functions. Examples of automorphic functions in the case $M = \mathbf C$ are periodic functions (thus, the function \$ e ^ {2 \pi.