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008 150903s2011 gw | o |||| 0|eng d
020 _a9783642161520
_99783642161520
024 7 _a10.1007/9783642161520
_2doi
035 _avtls000355928
039 9 _a201509030943
_bVLOAD
_c201405060357
_dVLOAD
_y201402191206
_zstaff
040 _aMX-SnUAN
_bspa
_cMX-SnUAN
_erda
050 4 _aQA241-247.5
100 1 _aKöhler, Günter.
_eautor
_9341834
245 1 0 _aEta Products and Theta Series Identities /
_cby Günter Köhler.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2011.
300 _axxii, 622 páginas
_brecurso en línea.
336 _atexto
_btxt
_2rdacontent
337 _acomputadora
_bc
_2rdamedia
338 _arecurso en línea
_bcr
_2rdacarrier
347 _aarchivo de texto
_bPDF
_2rda
490 0 _aSpringer Monographs in Mathematics,
_x1439-7382
500 _aSpringer eBooks
505 0 _aIntroduction -- 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.
520 _aThis 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.
590 _aPara consulta fuera de la UANL se requiere clave de acceso remoto.
710 2 _aSpringerLink (Servicio en línea)
_9299170
776 0 8 _iEdición impresa:
_z9783642161513
856 4 0 _uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/978-3-642-16152-0
_zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
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999 _c303297
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