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Monday, May 4, 2020 | History

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

Discontinuous groups and automorphic functions.

J. Lehner

# Discontinuous groups and automorphic functions.

Written in English

Subjects:
• Automorphic functions,
• Discontinuous groups

• Edition Notes

Bibliography: p. 409-418.

Classifications The Physical Object Series Mathematical surveys,, no. 8, Mathematical surveys ;, no. 8. LC Classifications QA351 .L4 Pagination xi, 425 p. Number of Pages 425 Open Library OL5881030M LC Control Number 63011987

[5] Joseph Lehner, Discontinuous groups and automorphic functions, American Mathematical Society, Providence, Mathematical Reviews (MathSciNet): MR Zentralblatt MATH: [6] A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric riemannian spaces with applications to Diriehlet series, J. Indian Math.

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### Discontinuous groups and automorphic functions. by J. 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. 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 by: 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. 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 coronavirus.

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.

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 : Joseph Lehner. This concise three-part treatment introduces undergraduate and graduate students to the theory of Discontinuous groups and automorphic functions.

book 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 forms and.

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). 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 present volume consists of the. 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 Function", in. 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 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. 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.

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.

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. 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. 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, – 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 Function 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. 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, automorphic functions and.

Discrete groups and automorphic functions: proceedings of an instructional conference. Harvey (Ph. D.) Academic Press, - Mathematics - pages. 1 Review. From inside the book conjugate contains converges Corollary corresponding covering map cusp defined Definition denote differential Dirichlet region disc discontinuous discrete Reviews: 1.

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.

Algebraic Groups and Discontinuous Subgroups: Author: Armand Borel and George D. Mostow: Detail: Note: This book is not downloadable for free Published: eBook Contents Algebraic Groups, Arithmetic Groups - Arithmetic Properties of Algebraic Groups.

Adèle Groups - Automorphic Functions and Decomposition of. Joseph Lehner (29 OctoberNew York City – 5 AugustHaverford, PA) was a mathematician at Michigan State University (–), the University of Maryland (–), and the University of Pittsburgh (–).

He worked on automorphic functions and introduced Atkin–Lehner theory. Publications. Lehner, Joseph (), Discontinuous groups and automorphic functions Authority control: GND:ISNI:. 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. A book of the names and address of people living in a city. What are the functions of groups.

Wiki User 'Discontinuous groups and automorphic functions' -- subject(s): Automorphic. 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. 2 Automorphic representations and L-functions for GL(1,AQ)39 Automorphic forms for GL(1,AQ)39 The L-function of an automorphic form 45 The local L-functions and their functional equations 55 Classical L-functions and root numbers 60 Automorphic representations for GL(1,AQ)65 Hecke operators for GL(1,AQ) Key Words: Automorphic forms, discontinuous groups, Fourier expansion, H-groups.

L It is a result familiar in the theory of automorphic forms that an entire automorphic form of positive dimension on an H-group is identically zero (see sec. 2 for the definitions).

This follows immediately, forFile Size: 2MB. algebraic functions of one variable, C. Chevalley The algebraic theory of semigroups, Volume I, A.

Clifford and G. Preston The algebraic theory of semigroups, Volume II, A. Clifford and G. Preston 8 Discontinuous groups and automorphic functions, J. Lehner 9 Linear approximation, Arthur Sard 10 An introduction to the analytic. A brief history of automorphic function theory, ; Chapter I.

The group of motions of the hyperbolic plane and its properly discontinuous subgroups ; Chapter II. Discontinuous groups in three geometries. Fuchsian functions ; Chapter III. Fuchsian functions ; Chapter by: 2.

Letters from William Burnside to Robert Fricke: automorphic functions, and the emergence of the Burnside Problem. Archive for History of Exact Sciences, Clemens Adelmann. Eberhard H A Gerbracht.

Clemens Adelmann. Eberhard H A Gerbracht. This little book should be of interest both to historians seeking to understand the evolution of the theory of automorphic functions and to mathematicians working in the area, and thus it is a valuable addition to the (rather short) list of original source material available in English translation.

This edited volume presents a collection of carefully refereed articles covering the latest advances in Automorphic Forms and Number Theory, that were primarily developed from presentations given at the “International Conference on Automorphic Forms.

automorphic functions generalize the ones proposed in [14]. Properties derived in Section 2 for Z-almost automorphic functions allow us to simplify the proofs of some important results, some of them known for almost automorphic functions in the literature (see Theorem and [30, Lemma ]). We will see that to obtain almost automorphic.Joseph Lehner has written: 'Discontinuous groups and automorphic functions' -- subject(s): Automorphic functions Asked in Authors, Poets, and Playwrights What has the author Brooks Keiluweit.dynamics.

The mathematical technique we will use is the theory of automorphic forms in one variable. An introduction to the classical aspects of this theory may be found in the books by Fricke and Klein (, ) and by Ford ().

A more modern and very lucid survey of the subject is the book ‘Discontinuous Groups and Automorphic.