Eta products and theta series identities
This monograph deals with products of Dedekind's eta function, with Hecke theta series on quadratic number fields, and with Eisenstein series. The author brings to the public the large number of identities that have been discovered over the past 20 years, the majority of which have not been pub...
Guardat en:
| Autor principal: | |
|---|---|
| Format: | Livre numérique |
| Idioma: | Anglais |
| Publicat: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Edició: | 1st ed. 2011. |
| Col·lecció: | Springer Monographs in Mathematics
|
| Matèries: | |
| Accés en línia: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Description d'après consultation du 18 février 2013 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Eta products and Theta series identities, Günter Köhler, 2011, Berlin, Springer, 1 vol. (XXI-621 p.), Springer monographs in mathematics, 978-3-642-16151-3 • Eta products and Theta series identities, Günter Köhler, 2011, Berlin, Springer, 1 vol. (XXI-621 p.), Springer monographs in mathematics, 978-3-642-16151-3 • Eta products and Theta series identities, Günter Köhler, 2011, Berlin, Springer, 1 vol. (XXI-621 p.), Springer monographs in mathematics, 978-3-642-16151-3 • Eta Products and Theta Series Identities, Texte imprimé, 9783642161537 |
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| 009 | PPN149908172 | ||
| 020 | |a 9783642161520 | ||
| 041 | 0 | |a eng | |
| 082 | |a 512.7 | ||
| 084 | |a 11-02. 2010 | ||
| 084 | |a 11F20. 2010 | ||
| 084 | |a 11F27. 2010 | ||
| 084 | |a 11R11. 2010 | ||
| 100 | 1 | |a Köhler, Günter, |d 1940- | |
| 245 | 1 | 0 | |a Eta products and theta series identities |c by Günter Köhler. |
| 250 | |a 1st ed. 2011. | ||
| 260 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Springer Monographs in Mathematics |x 2196-9922 | |
| 500 | |a Description d'après consultation du 18 février 2013 | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. Index | ||
| 505 | 1 | |a Introduction Part I: Theoretical background 1. Dedekind's eta function and modular forms 2. Eta products 3. Eta products and lattice points in simplices 4. An algorithm for listing lattice points in a simplex 5. Theta series with Hecke character 6. Groups of coprime residues in quadratic fields Part II: Examples.-7. Ideal numbers for quadratic fields 8 Eta products of weight 9. Level 1: The full modular group 10. The prime level N = 2 11. The prime level N = 3 12. Prime levels N = p >= 5 13. Level N = 4 14. Levels N = p2 with primes p >= 3 15 Levels N = p3 and p4 for primes p 16. Levels N = pq with primes 3 <= p < q 17. Weight 1 for levels N = 2p with primes p >= 5 18. Level N = 6 19. Weight 1 for prime power levels p5 and p6 20. Levels p2q for distinct primes p = 2 and q 21. Levels 4p for the primes p = 23 and 19 22. Levels 4p for p = 17 and 13 23. Levels 4p for p = 11 and 7 24. Weight 1 for level N = 20 25. Cuspidal eta products of weight 1 for level 12 26. Non-cuspidal eta products of weight 1 for level 12 27. Weight 1 for Fricke groups (q3p) 28. Weight 1 for Fricke groups (2pq) 29. Weight 1 for Fricke groups (p2q2) 30. Weight 1 for the Fricke groups (60) and (84) 31. Some more levels 4pq with odd primes p _= q References Directory of Characters Index of Notations Index. | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a This monograph deals with products of Dedekind's eta function, with Hecke theta series on quadratic number fields, and with Eisenstein series. The author brings to the public the large number of identities that have been discovered over the past 20 years, the majority of which have not been published elsewhere. The book will be of interest to graduate students and scholars in the field of number theory and, in particular, modular forms. It is not an introductory text in this field. Nevertheless, some theoretical background material is presented that is important for understanding the examples in Part II. In Part I relevant definitions and essential theorems -- such as a complete proof of the structure theorems for coprime residue class groups in quadratic number fields that are not easily accessible in the literature -- are provided. Another example is a thorough description of an algorithm for listing all eta products of given weight and level, together with proofs of some results on the bijection between these eta products and lattice simplices. | ||
| 650 | |a Nombres, Théorie des | ||
| 650 | |a Formes modulaires | ||
| 650 | |a Séries thêta | ||
| 776 | 0 | |0 149613733 |t Eta products and Theta series identities |f Günter Köhler |d 2011 |c Berlin |n Springer |p 1 vol. (XXI-621 p.) |s Springer monographs in mathematics |z 978-3-642-16151-3 | |
| 776 | 0 | |0 149613733 |t Eta products and Theta series identities |f Günter Köhler |d 2011 |c Berlin |n Springer |p 1 vol. (XXI-621 p.) |s Springer monographs in mathematics |z 978-3-642-16151-3 | |
| 776 | 0 | |0 149613733 |t Eta products and Theta series identities |f Günter Köhler |d 2011 |c Berlin |n Springer |p 1 vol. (XXI-621 p.) |s Springer monographs in mathematics |z 978-3-642-16151-3 | |
| 776 | 0 | |t Eta Products and Theta Series Identities |b Texte imprimé |z 9783642161537 | |
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| 856 | 4 | |u https://revue-sommaire.istex.fr/ark:/67375/8Q1-PCMJSH89-8 |z Accès sur la plateforme Istex | |
| 856 | 4 | |5 452349901:750622539 |u https://ezproxy.univ-orleans.fr/login?url=https://dx.doi.org/10.1007/978-3-642-16152-0 |z Accès Université d'Orléans | |
| 856 | 4 | |5 180339901:753980215 |u https://ezproxy.insa-cvl.fr/login?qurl=https://dx.doi.org/10.1007/978-3-642-16152-0 |z Accès INSA CVL | |
| 997 | |0 968265 |1 Livre numérique |a Ressource numérique |b INSA |b ENSA |c 0/Bibliothèque numérique/ |c 1/Bibliothèque numérique/Autre ressource numérique/ | ||