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| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783642161520 |
|
978-3-642-16152-0 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
|---|
| Classification number |
QA241-247.5 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
|---|
| Classification number |
512.7 |
| Edition number |
23 |
| 264 #1 - |
|---|
| -- |
Berlin, Heidelberg : |
| -- |
Springer Berlin Heidelberg, |
| -- |
2011. |
| 912 ## - |
|---|
| -- |
ZDB-2-SMA |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Köhler, Günter. |
| Relator term |
author. |
| 245 10 - IMMEDIATE SOURCE OF ACQUISITION NOTE |
|---|
| Title |
Eta Products and Theta Series Identities |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc |
by Günter Köhler. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
XXII, 622 p. |
| Other physical details |
online resource. |
| 440 1# - SERIES STATEMENT/ADDED ENTRY--TITLE |
|---|
| Title |
Springer Monographs in Mathematics, |
| International Standard Serial Number |
1439-7382 |
| 505 0# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
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. |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc |
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 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Mathematics. |
|
|---|
| Topical term or geographic name as entry element |
Number theory. |
|
|---|
| Topical term or geographic name as entry element |
Algebraic topology. |
|
|---|
| Topical term or geographic name as entry element |
Mathematics. |
|
|---|
| Topical term or geographic name as entry element |
Number Theory. |
|
|---|
| Topical term or geographic name as entry element |
Algebraic Topology. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
|---|
| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
|---|
| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Display text |
Printed edition: |
| International Standard Book Number |
9783642161513 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Uniform Resource Identifier |
http://dx.doi.org/10.1007/978-3-642-16152-0 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
|---|
| Source of classification or shelving scheme |
|
| Item type |
E-Book |
