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The Resource Automorphic Forms, by Anton Deitmar, (electronic resource)
Automorphic Forms, by Anton Deitmar, (electronic resource)
Resource Information
The item Automorphic Forms, by Anton Deitmar, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Automorphic Forms, by Anton Deitmar, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 Automorphic forms are an important complex analytic tool in number theory and modern arithmetic geometry. They played for example a vital role in Andrew Wiles's proof of Fermat's Last Theorem. This text provides a concise introduction to the world of automorphic forms using two approaches: the classic elementary theory and the modern point of view of adeles and representation theory. The reader will learn the important aims and results of the theory by focussing on its essential aspects and restricting it to the 'base field' of rational numbers. Students interested for example in arithmetic geometry or number theory will find that this book provides an optimal and easily accessible introduction into this topic
 Language

 eng
 eng
 Edition
 1st ed. 2012.
 Extent
 1 online resource (254 p.)
 Note
 Description based upon print version of record
 Contents

 Automorphic Forms; Introduction; Contents; Notation; Chapter 1: Doubly Periodic Functions; 1.1 Definition and First Properties; 1.2 The pFunction of Weierstrass; 1.3 The Differential Equation of the pFunction; 1.4 Eisenstein Series; 1.5 Bernoulli Numbers and Values of the Zeta Function; 1.6 Exercises and Remarks; Remarks; Chapter 2: Modular Forms for SL2(Z); 2.1 The Modular Group; 2.2 Modular Forms; 2.3 Estimating Fourier Coefficients; 2.4 LFunctions; 2.5 Hecke Operators; 2.6 Congruence Subgroups; 2.7 Nonholomorphic Eisenstein Series; 2.8 Maaß Wave Forms; 2.9 Exercises and Remarks; Remarks
 Chapter 3: Representations of SL2(R)3.1 Haar Measures and Decompositions; 3.1.1 The Modular Function; 3.2 Representations; 3.3 Modular Forms as Representation Vectors; 3.4 The Exponential Map; 3.5 Exercises and Remarks; Remarks; Chapter 4: pAdic Numbers; 4.1 Absolute Values; 4.2 Qp as Completion of Q; 4.3 Power Series; 4.4 Haar Measures; 4.5 Direct and Projective Limits; 4.6 Exercises; Chapter 5: Adeles and Ideles; 5.1 Restricted Products; 5.2 Adeles; 5.3 Ideles; 5.4 Fourier Analysis on A; 5.4.1 Local Fourier Analysis; 5.4.2 Global Fourier Analysis; 5.5 Exercises; Chapter 6: Tate's Thesis
 6.1 Poisson Summation Formula and the Riemann Zeta Function6.2 Zeta Functions in the Adelic Setting; 6.3 Dirichlet LFunctions; 6.4 Galois Representations and LFunctions; 6.5 Exercises; Chapter 7: Automorphic Representations of GL2(A); 7.1 Principal Series Representations; 7.2 From Real to Adelic; 7.3 Bochner Integral, Compact Operators and ArzelaAscoli; 7.3.1 The ArzelaAscoli Theorem; 7.4 Cusp Forms; 7.5 The Tensor Product Theorem; 7.5.1 Synthesis; 7.5.2 Analysis; 7.5.3 Admissibility of Automorphic Representations; 7.6 Exercises and Remarks; Remarks; Chapter 8: Automorphic LFunctions
 8.1 The Lattice M2(Q)8.2 Local Factors; 8.3 Global LFunctions; 8.4 The Example of Classical Cusp Forms; 8.5 Exercises and Remarks; Remarks; Appendix: Measure and Integration; A.1 Measurable Functions and Integration; A.2 Fubini's Theorem; A.3 LpSpaces; References; Index
 Isbn
 9781447144359
 Label
 Automorphic Forms
 Title
 Automorphic Forms
 Statement of responsibility
 by Anton Deitmar
 Language

 eng
 eng
 Summary
 Automorphic forms are an important complex analytic tool in number theory and modern arithmetic geometry. They played for example a vital role in Andrew Wiles's proof of Fermat's Last Theorem. This text provides a concise introduction to the world of automorphic forms using two approaches: the classic elementary theory and the modern point of view of adeles and representation theory. The reader will learn the important aims and results of the theory by focussing on its essential aspects and restricting it to the 'base field' of rational numbers. Students interested for example in arithmetic geometry or number theory will find that this book provides an optimal and easily accessible introduction into this topic
 http://library.link/vocab/creatorName
 Deitmar, Anton
 Dewey number
 516.353
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
 kmDZLycm8Q
 Language note
 English
 LC call number
 QA1939
 Literary form
 non fiction
 Nature of contents
 dictionaries
 Series statement
 Universitext,
 http://library.link/vocab/subjectName

 Mathematics
 Number theory
 Group theory
 Algebra
 Mathematics, general
 Number Theory
 Group Theory and Generalizations
 Algebra
 Label
 Automorphic Forms, by Anton Deitmar, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code
 cr
 Content category
 text
 Content type code
 txt
 Contents

 Automorphic Forms; Introduction; Contents; Notation; Chapter 1: Doubly Periodic Functions; 1.1 Definition and First Properties; 1.2 The pFunction of Weierstrass; 1.3 The Differential Equation of the pFunction; 1.4 Eisenstein Series; 1.5 Bernoulli Numbers and Values of the Zeta Function; 1.6 Exercises and Remarks; Remarks; Chapter 2: Modular Forms for SL2(Z); 2.1 The Modular Group; 2.2 Modular Forms; 2.3 Estimating Fourier Coefficients; 2.4 LFunctions; 2.5 Hecke Operators; 2.6 Congruence Subgroups; 2.7 Nonholomorphic Eisenstein Series; 2.8 Maaß Wave Forms; 2.9 Exercises and Remarks; Remarks
 Chapter 3: Representations of SL2(R)3.1 Haar Measures and Decompositions; 3.1.1 The Modular Function; 3.2 Representations; 3.3 Modular Forms as Representation Vectors; 3.4 The Exponential Map; 3.5 Exercises and Remarks; Remarks; Chapter 4: pAdic Numbers; 4.1 Absolute Values; 4.2 Qp as Completion of Q; 4.3 Power Series; 4.4 Haar Measures; 4.5 Direct and Projective Limits; 4.6 Exercises; Chapter 5: Adeles and Ideles; 5.1 Restricted Products; 5.2 Adeles; 5.3 Ideles; 5.4 Fourier Analysis on A; 5.4.1 Local Fourier Analysis; 5.4.2 Global Fourier Analysis; 5.5 Exercises; Chapter 6: Tate's Thesis
 6.1 Poisson Summation Formula and the Riemann Zeta Function6.2 Zeta Functions in the Adelic Setting; 6.3 Dirichlet LFunctions; 6.4 Galois Representations and LFunctions; 6.5 Exercises; Chapter 7: Automorphic Representations of GL2(A); 7.1 Principal Series Representations; 7.2 From Real to Adelic; 7.3 Bochner Integral, Compact Operators and ArzelaAscoli; 7.3.1 The ArzelaAscoli Theorem; 7.4 Cusp Forms; 7.5 The Tensor Product Theorem; 7.5.1 Synthesis; 7.5.2 Analysis; 7.5.3 Admissibility of Automorphic Representations; 7.6 Exercises and Remarks; Remarks; Chapter 8: Automorphic LFunctions
 8.1 The Lattice M2(Q)8.2 Local Factors; 8.3 Global LFunctions; 8.4 The Example of Classical Cusp Forms; 8.5 Exercises and Remarks; Remarks; Appendix: Measure and Integration; A.1 Measurable Functions and Integration; A.2 Fubini's Theorem; A.3 LpSpaces; References; Index
 Dimensions
 unknown
 Edition
 1st ed. 2012.
 Extent
 1 online resource (254 p.)
 Form of item
 online
 Isbn
 9781447144359
 Media category
 computer
 Media type code
 c
 Other control number
 10.1007/9781447144359
 Specific material designation
 remote
 System control number

 (CKB)3390000000030149
 (EBL)1030652
 (OCoLC)809543581
 (SSID)ssj0000745843
 (PQKBManifestationID)11495888
 (PQKBTitleCode)TC0000745843
 (PQKBWorkID)10859454
 (PQKB)10684249
 (DEHe213)9781447144359
 (MiAaPQ)EBC1030652
 (EXLCZ)993390000000030149
 Label
 Automorphic Forms, by Anton Deitmar, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code
 cr
 Content category
 text
 Content type code
 txt
 Contents

 Automorphic Forms; Introduction; Contents; Notation; Chapter 1: Doubly Periodic Functions; 1.1 Definition and First Properties; 1.2 The pFunction of Weierstrass; 1.3 The Differential Equation of the pFunction; 1.4 Eisenstein Series; 1.5 Bernoulli Numbers and Values of the Zeta Function; 1.6 Exercises and Remarks; Remarks; Chapter 2: Modular Forms for SL2(Z); 2.1 The Modular Group; 2.2 Modular Forms; 2.3 Estimating Fourier Coefficients; 2.4 LFunctions; 2.5 Hecke Operators; 2.6 Congruence Subgroups; 2.7 Nonholomorphic Eisenstein Series; 2.8 Maaß Wave Forms; 2.9 Exercises and Remarks; Remarks
 Chapter 3: Representations of SL2(R)3.1 Haar Measures and Decompositions; 3.1.1 The Modular Function; 3.2 Representations; 3.3 Modular Forms as Representation Vectors; 3.4 The Exponential Map; 3.5 Exercises and Remarks; Remarks; Chapter 4: pAdic Numbers; 4.1 Absolute Values; 4.2 Qp as Completion of Q; 4.3 Power Series; 4.4 Haar Measures; 4.5 Direct and Projective Limits; 4.6 Exercises; Chapter 5: Adeles and Ideles; 5.1 Restricted Products; 5.2 Adeles; 5.3 Ideles; 5.4 Fourier Analysis on A; 5.4.1 Local Fourier Analysis; 5.4.2 Global Fourier Analysis; 5.5 Exercises; Chapter 6: Tate's Thesis
 6.1 Poisson Summation Formula and the Riemann Zeta Function6.2 Zeta Functions in the Adelic Setting; 6.3 Dirichlet LFunctions; 6.4 Galois Representations and LFunctions; 6.5 Exercises; Chapter 7: Automorphic Representations of GL2(A); 7.1 Principal Series Representations; 7.2 From Real to Adelic; 7.3 Bochner Integral, Compact Operators and ArzelaAscoli; 7.3.1 The ArzelaAscoli Theorem; 7.4 Cusp Forms; 7.5 The Tensor Product Theorem; 7.5.1 Synthesis; 7.5.2 Analysis; 7.5.3 Admissibility of Automorphic Representations; 7.6 Exercises and Remarks; Remarks; Chapter 8: Automorphic LFunctions
 8.1 The Lattice M2(Q)8.2 Local Factors; 8.3 Global LFunctions; 8.4 The Example of Classical Cusp Forms; 8.5 Exercises and Remarks; Remarks; Appendix: Measure and Integration; A.1 Measurable Functions and Integration; A.2 Fubini's Theorem; A.3 LpSpaces; References; Index
 Dimensions
 unknown
 Edition
 1st ed. 2012.
 Extent
 1 online resource (254 p.)
 Form of item
 online
 Isbn
 9781447144359
 Media category
 computer
 Media type code
 c
 Other control number
 10.1007/9781447144359
 Specific material designation
 remote
 System control number

 (CKB)3390000000030149
 (EBL)1030652
 (OCoLC)809543581
 (SSID)ssj0000745843
 (PQKBManifestationID)11495888
 (PQKBTitleCode)TC0000745843
 (PQKBWorkID)10859454
 (PQKB)10684249
 (DEHe213)9781447144359
 (MiAaPQ)EBC1030652
 (EXLCZ)993390000000030149
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