Modular forms :: a classical and computational introduction /
"This book presents a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. It also includes applications of modular forms to such diverse subjects as the theory of qu...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
London ; Hackensack, NJ :
Imperial College Press,
©2008.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "This book presents a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. It also includes applications of modular forms to such diverse subjects as the theory of quadratic forms, the proof of Fermat's last theorem and the approximation of pi. It provides a balanced overview of both the theoretical and computational sides of the subject, allowing a variety of courses to be taught from it."--Jacket |
| Beschreibung: | "This book is based on notes for lectures given at the Mathematical Institute at the University of Oxford ... 2004-2007"--Introduction |
| Beschreibung: | 1 online resource (xii, 224 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 205-216) and index. |
| ISBN: | 9781848162143 1848162146 |
Internformat
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| 245 | 1 | 0 | |a Modular forms : |b a classical and computational introduction / |c L.J.P. Kilford. |
| 260 | |a London ; |a Hackensack, NJ : |b Imperial College Press, |c ©2008. | ||
| 300 | |a 1 online resource (xii, 224 pages) : |b illustrations | ||
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| 500 | |a "This book is based on notes for lectures given at the Mathematical Institute at the University of Oxford ... 2004-2007"--Introduction | ||
| 504 | |a Includes bibliographical references (pages 205-216) and index. | ||
| 520 | 1 | |a "This book presents a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. It also includes applications of modular forms to such diverse subjects as the theory of quadratic forms, the proof of Fermat's last theorem and the approximation of pi. It provides a balanced overview of both the theoretical and computational sides of the subject, allowing a variety of courses to be taught from it."--Jacket | |
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 1. Historical overview. 1.1. 18th century -- a prologue. 1.2. 19th century -- the classical period. 1.3. Early 20th century -- arithmetic applications. 1.4. Later 20th century -- the link to elliptic curves. 1.5. The 21st century -- the Langlands program -- 2. Introduction to modular forms. 2.1. Modular forms for [symbol]. 2.2. Eisenstein series for the full modular group. 2.3. Computing Fourier expansions of Eisenstein series. 2.4. Congruence subgroups. 2.5. Fundamental domains. 2.6. Modular forms for congruence subgroups. 2.7. Eisenstein series for congruence subgroups. 2.8. Derivatives of modular forms. 2.9. Exercises -- 3. Results on finite-dimensionality. 3.1. Spaces of modular forms are finite-dimensional. 3.2. Explicit formulae for the dimensions of spaces of modular forms. 3.3. The Sturm bound. 3.4. Exercises -- 4. The arithmetic of modular forms. 4.1. Hecke operators. 4.2. Bases of eigenforms. 4.3. Oldforms and newforms. 4.4. Exercises -- 5. Applications of modular forms. 5.1. Modular functions. 5.2. [symbol]-products and [symbol]-quotients. 5.3. The arithmetric of the [symbol]-invariant. 5.4. Applications of the modular function [symbol]. 5.5. Identities of series and products. 5.6. The Ramanujan-Petersson conjecture. 5.7. Elliptic curves and modular forms. 5.8. Theta functions and their applications. 5.9. CM modular forms. 5.10. Lacunary modular forms. 5.11. Exercises -- 6. Modular forms in characteristic [symbol]. 6.1. Classical treatment. 6.2. Galois representations attached to mod [symbol] modular forms. 6.3. Katz modular forms. 6.4. The Sturm bound in characteristic [symbol]. 6.5. Computations with mod [symbol] modular forms. 6.6. Exercises -- 7. Computing with modular forms. 7.1. Historical introduction to computations in number theory. 7.2. MAGMA. 7.3. SAGE. 7.4. PARI and other systems. 7.5. Discussion of computation. 7.6. Exercises. | |
| 650 | 0 | |a Forms, Modular |x Data processing. | |
| 650 | 0 | |a Algebraic spaces |x Data processing. | |
| 650 | 6 | |a Formes modulaires |x Informatique. | |
| 650 | 6 | |a Espaces algébriques |x Informatique. | |
| 650 | 7 | |a MATHEMATICS |x Number Theory. |2 bisacsh | |
| 758 | |i has work: |a Modular forms (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGpywfD8Rxj7F3TRPqkPXq |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
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Datensatz im Suchindex
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| author | Kilford, L. J. P. (Lloyd James Peter) |
| author_GND | http://id.loc.gov/authorities/names/no2008168688 |
| author_facet | Kilford, L. J. P. (Lloyd James Peter) |
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| callnumber-label | QA243 |
| callnumber-raw | QA243 .K54 2008eb |
| callnumber-search | QA243 .K54 2008eb |
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| callnumber-subject | QA - Mathematics |
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| contents | 1. Historical overview. 1.1. 18th century -- a prologue. 1.2. 19th century -- the classical period. 1.3. Early 20th century -- arithmetic applications. 1.4. Later 20th century -- the link to elliptic curves. 1.5. The 21st century -- the Langlands program -- 2. Introduction to modular forms. 2.1. Modular forms for [symbol]. 2.2. Eisenstein series for the full modular group. 2.3. Computing Fourier expansions of Eisenstein series. 2.4. Congruence subgroups. 2.5. Fundamental domains. 2.6. Modular forms for congruence subgroups. 2.7. Eisenstein series for congruence subgroups. 2.8. Derivatives of modular forms. 2.9. Exercises -- 3. Results on finite-dimensionality. 3.1. Spaces of modular forms are finite-dimensional. 3.2. Explicit formulae for the dimensions of spaces of modular forms. 3.3. The Sturm bound. 3.4. Exercises -- 4. The arithmetic of modular forms. 4.1. Hecke operators. 4.2. Bases of eigenforms. 4.3. Oldforms and newforms. 4.4. Exercises -- 5. Applications of modular forms. 5.1. Modular functions. 5.2. [symbol]-products and [symbol]-quotients. 5.3. The arithmetric of the [symbol]-invariant. 5.4. Applications of the modular function [symbol]. 5.5. Identities of series and products. 5.6. The Ramanujan-Petersson conjecture. 5.7. Elliptic curves and modular forms. 5.8. Theta functions and their applications. 5.9. CM modular forms. 5.10. Lacunary modular forms. 5.11. Exercises -- 6. Modular forms in characteristic [symbol]. 6.1. Classical treatment. 6.2. Galois representations attached to mod [symbol] modular forms. 6.3. Katz modular forms. 6.4. The Sturm bound in characteristic [symbol]. 6.5. Computations with mod [symbol] modular forms. 6.6. Exercises -- 7. Computing with modular forms. 7.1. Historical introduction to computations in number theory. 7.2. MAGMA. 7.3. SAGE. 7.4. PARI and other systems. 7.5. Discussion of computation. 7.6. Exercises. |
| ctrlnum | (OCoLC)827947324 |
| dewey-full | 512.73 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.73 |
| dewey-search | 512.73 |
| dewey-sort | 3512.73 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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Galois representations attached to mod [symbol] modular forms. 6.3. Katz modular forms. 6.4. The Sturm bound in characteristic [symbol]. 6.5. Computations with mod [symbol] modular forms. 6.6. Exercises -- 7. Computing with modular forms. 7.1. Historical introduction to computations in number theory. 7.2. MAGMA. 7.3. SAGE. 7.4. PARI and other systems. 7.5. Discussion of computation. 7.6. 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| id | ZDB-4-EBA-ocn827947324 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:11Z |
| institution | BVB |
| isbn | 9781848162143 1848162146 |
| language | English |
| oclc_num | 827947324 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xii, 224 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Imperial College Press, |
| record_format | marc |
| spelling | Kilford, L. J. P. (Lloyd James Peter) https://id.oclc.org/worldcat/entity/E39PCjHPFP4x4KC7h3j3m387VC http://id.loc.gov/authorities/names/no2008168688 Modular forms : a classical and computational introduction / L.J.P. Kilford. London ; Hackensack, NJ : Imperial College Press, ©2008. 1 online resource (xii, 224 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier "This book is based on notes for lectures given at the Mathematical Institute at the University of Oxford ... 2004-2007"--Introduction Includes bibliographical references (pages 205-216) and index. "This book presents a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. It also includes applications of modular forms to such diverse subjects as the theory of quadratic forms, the proof of Fermat's last theorem and the approximation of pi. It provides a balanced overview of both the theoretical and computational sides of the subject, allowing a variety of courses to be taught from it."--Jacket Print version record. 1. Historical overview. 1.1. 18th century -- a prologue. 1.2. 19th century -- the classical period. 1.3. Early 20th century -- arithmetic applications. 1.4. Later 20th century -- the link to elliptic curves. 1.5. The 21st century -- the Langlands program -- 2. Introduction to modular forms. 2.1. Modular forms for [symbol]. 2.2. Eisenstein series for the full modular group. 2.3. Computing Fourier expansions of Eisenstein series. 2.4. Congruence subgroups. 2.5. Fundamental domains. 2.6. Modular forms for congruence subgroups. 2.7. Eisenstein series for congruence subgroups. 2.8. Derivatives of modular forms. 2.9. Exercises -- 3. Results on finite-dimensionality. 3.1. Spaces of modular forms are finite-dimensional. 3.2. Explicit formulae for the dimensions of spaces of modular forms. 3.3. The Sturm bound. 3.4. Exercises -- 4. The arithmetic of modular forms. 4.1. Hecke operators. 4.2. Bases of eigenforms. 4.3. Oldforms and newforms. 4.4. Exercises -- 5. Applications of modular forms. 5.1. Modular functions. 5.2. [symbol]-products and [symbol]-quotients. 5.3. The arithmetric of the [symbol]-invariant. 5.4. Applications of the modular function [symbol]. 5.5. Identities of series and products. 5.6. The Ramanujan-Petersson conjecture. 5.7. Elliptic curves and modular forms. 5.8. Theta functions and their applications. 5.9. CM modular forms. 5.10. Lacunary modular forms. 5.11. Exercises -- 6. Modular forms in characteristic [symbol]. 6.1. Classical treatment. 6.2. Galois representations attached to mod [symbol] modular forms. 6.3. Katz modular forms. 6.4. The Sturm bound in characteristic [symbol]. 6.5. Computations with mod [symbol] modular forms. 6.6. Exercises -- 7. Computing with modular forms. 7.1. Historical introduction to computations in number theory. 7.2. MAGMA. 7.3. SAGE. 7.4. PARI and other systems. 7.5. Discussion of computation. 7.6. Exercises. Forms, Modular Data processing. Algebraic spaces Data processing. Formes modulaires Informatique. Espaces algébriques Informatique. MATHEMATICS Number Theory. bisacsh has work: Modular forms (Text) https://id.oclc.org/worldcat/entity/E39PCGpywfD8Rxj7F3TRPqkPXq https://id.oclc.org/worldcat/ontology/hasWork Print version: Kilford, L.J.P. (Lloyd James Peter). Modular forms. London ; Hackensack, NJ : Imperial College Press, ©2008 1848162138 (DLC) 2008301117 (OCoLC)234380364 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=516755 Volltext |
| spellingShingle | Kilford, L. J. P. (Lloyd James Peter) Modular forms : a classical and computational introduction / 1. Historical overview. 1.1. 18th century -- a prologue. 1.2. 19th century -- the classical period. 1.3. Early 20th century -- arithmetic applications. 1.4. Later 20th century -- the link to elliptic curves. 1.5. The 21st century -- the Langlands program -- 2. Introduction to modular forms. 2.1. Modular forms for [symbol]. 2.2. Eisenstein series for the full modular group. 2.3. Computing Fourier expansions of Eisenstein series. 2.4. Congruence subgroups. 2.5. Fundamental domains. 2.6. Modular forms for congruence subgroups. 2.7. Eisenstein series for congruence subgroups. 2.8. Derivatives of modular forms. 2.9. Exercises -- 3. Results on finite-dimensionality. 3.1. Spaces of modular forms are finite-dimensional. 3.2. Explicit formulae for the dimensions of spaces of modular forms. 3.3. The Sturm bound. 3.4. Exercises -- 4. The arithmetic of modular forms. 4.1. Hecke operators. 4.2. Bases of eigenforms. 4.3. Oldforms and newforms. 4.4. Exercises -- 5. Applications of modular forms. 5.1. Modular functions. 5.2. [symbol]-products and [symbol]-quotients. 5.3. The arithmetric of the [symbol]-invariant. 5.4. Applications of the modular function [symbol]. 5.5. Identities of series and products. 5.6. The Ramanujan-Petersson conjecture. 5.7. Elliptic curves and modular forms. 5.8. Theta functions and their applications. 5.9. CM modular forms. 5.10. Lacunary modular forms. 5.11. Exercises -- 6. Modular forms in characteristic [symbol]. 6.1. Classical treatment. 6.2. Galois representations attached to mod [symbol] modular forms. 6.3. Katz modular forms. 6.4. The Sturm bound in characteristic [symbol]. 6.5. Computations with mod [symbol] modular forms. 6.6. Exercises -- 7. Computing with modular forms. 7.1. Historical introduction to computations in number theory. 7.2. MAGMA. 7.3. SAGE. 7.4. PARI and other systems. 7.5. Discussion of computation. 7.6. Exercises. Forms, Modular Data processing. Algebraic spaces Data processing. Formes modulaires Informatique. Espaces algébriques Informatique. MATHEMATICS Number Theory. bisacsh |
| title | Modular forms : a classical and computational introduction / |
| title_auth | Modular forms : a classical and computational introduction / |
| title_exact_search | Modular forms : a classical and computational introduction / |
| title_full | Modular forms : a classical and computational introduction / L.J.P. Kilford. |
| title_fullStr | Modular forms : a classical and computational introduction / L.J.P. Kilford. |
| title_full_unstemmed | Modular forms : a classical and computational introduction / L.J.P. Kilford. |
| title_short | Modular forms : |
| title_sort | modular forms a classical and computational introduction |
| title_sub | a classical and computational introduction / |
| topic | Forms, Modular Data processing. Algebraic spaces Data processing. Formes modulaires Informatique. Espaces algébriques Informatique. MATHEMATICS Number Theory. bisacsh |
| topic_facet | Forms, Modular Data processing. Algebraic spaces Data processing. Formes modulaires Informatique. Espaces algébriques Informatique. MATHEMATICS Number Theory. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=516755 |
| work_keys_str_mv | AT kilfordljp modularformsaclassicalandcomputationalintroduction |