The Resource Automorphic Forms, by Anton Deitmar, (electronic resource)

Automorphic Forms, by Anton Deitmar, (electronic resource)

Label
Automorphic Forms
Title
Automorphic Forms
Statement of responsibility
by Anton Deitmar
Creator
Author
Author
Subject
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
Member of
http://library.link/vocab/creatorName
Deitmar, Anton
Dewey number
516.353
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
-kmDZLycm8Q
Language note
English
LC call number
QA1-939
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)
Instantiates
Publication
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 p-Function of Weierstrass; 1.3 The Differential Equation of the p-Function; 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 L-Functions; 2.5 Hecke Operators; 2.6 Congruence Subgroups; 2.7 Non-holomorphic 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: p-Adic 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 L-Functions; 6.4 Galois Representations and L-Functions; 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 Arzela-Ascoli; 7.3.1 The Arzela-Ascoli 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 L-Functions
  • 8.1 The Lattice M2(Q)8.2 Local Factors; 8.3 Global L-Functions; 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 Lp-Spaces; 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
10.1007/978-1-4471-4435-9
Specific material designation
remote
System control number
  • (CKB)3390000000030149
  • (EBL)1030652
  • (OCoLC)809543581
  • (SSID)ssj0000745843
  • (PQKBManifestationID)11495888
  • (PQKBTitleCode)TC0000745843
  • (PQKBWorkID)10859454
  • (PQKB)10684249
  • (DE-He213)978-1-4471-4435-9
  • (MiAaPQ)EBC1030652
  • (EXLCZ)993390000000030149
Label
Automorphic Forms, by Anton Deitmar, (electronic resource)
Publication
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 p-Function of Weierstrass; 1.3 The Differential Equation of the p-Function; 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 L-Functions; 2.5 Hecke Operators; 2.6 Congruence Subgroups; 2.7 Non-holomorphic 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: p-Adic 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 L-Functions; 6.4 Galois Representations and L-Functions; 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 Arzela-Ascoli; 7.3.1 The Arzela-Ascoli 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 L-Functions
  • 8.1 The Lattice M2(Q)8.2 Local Factors; 8.3 Global L-Functions; 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 Lp-Spaces; 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
10.1007/978-1-4471-4435-9
Specific material designation
remote
System control number
  • (CKB)3390000000030149
  • (EBL)1030652
  • (OCoLC)809543581
  • (SSID)ssj0000745843
  • (PQKBManifestationID)11495888
  • (PQKBTitleCode)TC0000745843
  • (PQKBWorkID)10859454
  • (PQKB)10684249
  • (DE-He213)978-1-4471-4435-9
  • (MiAaPQ)EBC1030652
  • (EXLCZ)993390000000030149

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