skip to content
Elliptic modular functions : an introduction Preview this item
ClosePreview this item
Checking...

Elliptic modular functions : an introduction

Author: Bruno Schoeneberg; James R Smart; E A Schwandt
Publisher: Berlin ; New York : Springer, 1974.
Series: Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellung, 203
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

 

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Document Type: Book
All Authors / Contributors: Bruno Schoeneberg; James R Smart; E A Schwandt
ISBN: 354006382X 9783540063827 038706382X 9780387063829
OCLC Number: 468124084
Notes: Bibliogr. p. 227-229. Index.
Description: 232 p. ; 24 cm.
Contents: I. The Modular Group.- 1. Inhomogeneous Linear Transformations.- 2. Homogeneous Linear Transformations.- 3. The Modular Group. Fixed Points.- 4. Generators and Relations.- 5. Fundamental Region.- II. The Modular Functions of Level One.- 1. Definition and Properties of Modular Functions.- 2. Extension of the Modular Group by Reflections.- 3. Existence of Modular Functions. The Absolute Modular Invariant J.- 4. Modular Form.- 5. Entire Modular Forms.- III. Eisenstein Series.- 1. The Eisenstein Series in the Case of Absolute Convergence.- 2. The Eisenstein Series in the Case of Conditional Convergence.- 3. The Discriminant ?.- IV. Subgroups of the Modular Group.- 1. Subgroups of the Modular Group.- 2. The Principal Congruence Groups.- 3. Congruence Groups.- 4. Fundamental Region.- 5. Fundamental Regions for Special Subgroups.- 6. The Quotient Space ?*/?1.- 7. Genus of the Fundamental Region.- 8. The Genus of the Fundamental Region of ?0(N).- V. Function Theory for the Subgroups of Finite Index in the Modular Group.- 1. Functions for Subgroups.- 2. Modular Forms for Subgroups.- 3. Modular Forms of Dimension ?2 and Integrals.- 4. The Riemann-Roch Theorem and Applications.- VI. Fields of Modular Functions.- 1. Algebraic Field Extensions of ?(J).- 2. The Fields ?$$ \left( {\sqrt {J - 1} } \right) $$ and ?$$ \left( {{}^3\sqrt J } \right) $$.- 3. Transformation Groups of Order n.- 4. Transformation Fields of Order n.- 5. The Modular Equation of Order n.- 6. The Galois Group of the Modular Equation.- 7. Transformations of Order n for Modular Forms.- VII. Eisenstein Series of Higher Level.- 1. The Series in the Case of Absolute Convergence.- 2. The Series of Dimension ?1 and ?2.- 3. Properties of the Series of Dimension ?1 and ?2. Applications.- 4. Division Equation.- VIII. The Integrals of ?-Division Values.- 1. The Space of ?-Division Values. Integrals.- 2. An Asymptotic Formula and the Behavior of the Integrals under the Transformation T.- 3. A Second Look at the Behavior of the Integrals under the Transformation T. The General Transformation Formula.- 4. Consequences of the Transformation Formula.- IX. Theta Series.- 1. General Theta Series. An Operator.- 2. Special Theta Series.- 3. Behavior of the Theta Series under Modular Transformations.- 4. Behavior of the Theta Series under Congruence Groups. Gaussian Sums.- 5. Examples and Applications.- Literature.- Index of Definitions.- Index of Notations.
Series Title: Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellung, 203
Responsibility: B. Schoeneberg ; transl. from the German by J.R. Smart and E.A. Schwandt.
More information:

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/468124084> # Elliptic modular functions : an introduction
    a schema:CreativeWork, schema:Book ;
   library:oclcnum "468124084" ;
   library:placeOfPublication <http://id.loc.gov/vocabulary/countries/vp> ;
   library:placeOfPublication <http://dbpedia.org/resource/New_York_City> ; # New York
   library:placeOfPublication <http://experiment.worldcat.org/entity/work/data/364486543#Place/berlin> ; # Berlin
   schema:about <http://experiment.worldcat.org/entity/work/data/364486543#Topic/fonction_elliptique> ; # fonction elliptique
   schema:about <http://dewey.info/class/515.982/e22/> ;
   schema:about <http://experiment.worldcat.org/entity/work/data/364486543#Topic/serie_eisenstein> ; # série Eisenstein
   schema:about <http://experiment.worldcat.org/entity/work/data/364486543#Topic/fonctions_modulaires> ; # Fonctions modulaires
   schema:about <http://experiment.worldcat.org/entity/work/data/364486543#Topic/groupes_modulaires> ; # Groupes modulaires
   schema:about <http://experiment.worldcat.org/entity/work/data/364486543#Topic/fonction_modulaire> ; # fonction modulaire
   schema:about <http://experiment.worldcat.org/entity/work/data/364486543#Topic/theorie_fonction> ; # théorie fonction
   schema:about <http://experiment.worldcat.org/entity/work/data/364486543#Topic/groupe_modulaire> ; # groupe modulaire
   schema:about <http://experiment.worldcat.org/entity/work/data/364486543#Topic/fonctions_elliptiques> ; # Fonctions elliptiques
   schema:about <http://experiment.worldcat.org/entity/work/data/364486543#Topic/fonction_theta> ; # fonction théta
   schema:author <http://viaf.org/viaf/9922496> ; # Bruno Schoeneberg
   schema:bookFormat bgn:PrintBook ;
   schema:contributor <http://experiment.worldcat.org/entity/work/data/364486543#Person/smart_james_r_1930> ; # James R. Smart
   schema:contributor <http://viaf.org/viaf/166282979> ; # E. A. Schwandt
   schema:datePublished "1974" ;
   schema:exampleOfWork <http://worldcat.org/entity/work/id/364486543> ;
   schema:inLanguage "en" ;
   schema:isPartOf <http://experiment.worldcat.org/entity/work/data/364486543#Series/die_grundlehren_der_mathematischen_wissenschaften_in_einzeldarstellung> ; # Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellung ;
   schema:name "Elliptic modular functions : an introduction" ;
   schema:numberOfPages "232" ;
   schema:productID "468124084" ;
   schema:publication <http://www.worldcat.org/title/-/oclc/468124084#PublicationEvent/berlin_new_york_springer_1974> ;
   schema:publisher <http://experiment.worldcat.org/entity/work/data/364486543#Agent/springer> ; # Springer
   schema:workExample <http://worldcat.org/isbn/9783540063827> ;
   schema:workExample <http://worldcat.org/isbn/9780387063829> ;
   wdrs:describedby <http://www.worldcat.org/title/-/oclc/468124084> ;
    .


Related Entities

<http://dbpedia.org/resource/New_York_City> # New York
    a schema:Place ;
   schema:name "New York" ;
    .

<http://experiment.worldcat.org/entity/work/data/364486543#Person/smart_james_r_1930> # James R. Smart
    a schema:Person ;
   schema:birthDate "1930" ;
   schema:deathDate "" ;
   schema:familyName "Smart" ;
   schema:givenName "James R." ;
   schema:name "James R. Smart" ;
    .

<http://experiment.worldcat.org/entity/work/data/364486543#Series/die_grundlehren_der_mathematischen_wissenschaften_in_einzeldarstellung> # Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellung ;
    a bgn:PublicationSeries ;
   schema:hasPart <http://www.worldcat.org/oclc/468124084> ; # Elliptic modular functions : an introduction
   schema:name "Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellung ;" ;
    .

<http://experiment.worldcat.org/entity/work/data/364486543#Topic/fonction_elliptique> # fonction elliptique
    a schema:Intangible ;
   schema:name "fonction elliptique" ;
    .

<http://experiment.worldcat.org/entity/work/data/364486543#Topic/fonctions_elliptiques> # Fonctions elliptiques
    a schema:Intangible ;
   schema:name "Fonctions elliptiques"@fr ;
    .

<http://experiment.worldcat.org/entity/work/data/364486543#Topic/fonctions_modulaires> # Fonctions modulaires
    a schema:Intangible ;
   schema:name "Fonctions modulaires" ;
   schema:name "Fonctions modulaires"@fr ;
    .

<http://viaf.org/viaf/166282979> # E. A. Schwandt
    a schema:Person ;
   schema:familyName "Schwandt" ;
   schema:givenName "E. A." ;
   schema:name "E. A. Schwandt" ;
    .

<http://viaf.org/viaf/9922496> # Bruno Schoeneberg
    a schema:Person ;
   schema:familyName "Schoeneberg" ;
   schema:givenName "Bruno" ;
   schema:name "Bruno Schoeneberg" ;
    .

<http://worldcat.org/isbn/9780387063829>
    a schema:ProductModel ;
   schema:isbn "038706382X" ;
   schema:isbn "9780387063829" ;
    .

<http://worldcat.org/isbn/9783540063827>
    a schema:ProductModel ;
   schema:isbn "354006382X" ;
   schema:isbn "9783540063827" ;
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.