Eta Products and Theta Series Identities

• Κύριος συγγραφέας: Köhler, Günter (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.
• Σειρά: Springer Monographs in Mathematics,
• Θέματα: Mathematics.; Number theory.; Algebraic topology.; Number Theory.; Algebraic Topology.

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...

Πίνακας περιεχομένων:

• 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 Γ∗(q3p)
• 28. Weight 1 for Fricke groups Γ∗(2pq)
• 29. Weight 1 for Fricke groups Γ∗(p2q2)
• 30. Weight 1 for the Fricke groups Γ∗(60) and Γ∗(84)
• 31. Some more levels 4pq with odd primes p _= q
• References
• Directory of Characters
• Index of Notations
• Index.