LEADER 02950nam 22004695 450 001 9910254273403321 005 20220329235045.0 010 $a3-319-56172-3 024 7 $a10.1007/978-3-319-56172-1 035 $a(CKB)3710000001404672 035 $a(DE-He213)978-3-319-56172-1 035 $a(MiAaPQ)EBC4876555 035 $a(PPN)20299371X 035 $a(EXLCZ)993710000001404672 100 $a20170612d2017 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aRamanujan's theta functions /$fby Shaun Cooper 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XVIII, 687 p. 1 illus.) 311 $a3-319-56171-5 320 $aIncludes bibliographical references and indexes. 327 $aPreface -- 0. Sum to Product Identities -- 1. Elliptic Functions -- 2. Transformations -- 3. Theta Functions -- 4. Levels 1, 2, 3, and 4: Jacobi's Inversion Theorem and Ramanujan's Alternative Theories -- 5. Level 5: The Rogers-Ramanujan Continued Fraction -- 6. Level 6: Ramanujan's Cubic Continued Fraction -- 7. Level 7 -- 8. Level 8: The Ramanujan-Gollnitz-Gordon Continued Fraction -- 9. Level 9 -- 10. Level 10: Ramanujan's Function k -- 11. Levels 11 and 23 -- 12. Level 12 -- 13. Hypergeometric Modular Transformations -- 14. Ramanujan's Series for 1/pi -- References. 330 $aTheta functions were studied extensively by Ramanujan. This book provides a systematic development of Ramanujan?s results and extends them to a general theory. The author?s treatment of the subject is comprehensive, providing a detailed study of theta functions and modular forms for levels up to 12. Aimed at advanced undergraduates, graduate students, and researchers, the organization, user-friendly presentation, and rich source of examples, lends this book to serve as a useful reference, a pedagogical tool, and a stimulus for further research. Topics, especially those discussed in the second half of the book, have been the subject of much recent research; many of which are appearing in book form for the first time. Further results are summarized in the numerous exercises at the end of each chapter. 606 $aNumber theory 606 $aGeometry, Algebraic 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 615 0$aNumber theory. 615 0$aGeometry, Algebraic. 615 14$aNumber Theory. 615 24$aAlgebraic Geometry. 676 $a512.7 700 $aCooper$b Shaun$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767406 906 $aBOOK 912 $a9910254273403321 996 $aRamanujan's Theta Functions$91562320 997 $aUNINA LEADER 01506nam0 22003251i 450 001 UON00524055 005 20240605125037.598 010 $a978-09-903136-1-8 100 $a20240416d2015 |0itac50 ba 101 $aeng 102 $aUS 105 $a|||| ||||| 200 1 $aTrolldom$espells and methods of the Norse folk magic tradition$fJohannes Björn Gårdbäck 205 $a1. ed 210 $aForestville$cThe Ironwode Institution for the Preservation and Popularization of Indigenous Ethnomagicology$eYIPPIE$d2015 215 $a288 p.$cill.$d26 cm. 606 $aFolklore$xScandinavia$3UONC103348$2FI 606 $aMagia$3UONC017448$2FI 606 $aStregoneria$3UONC103350$2FI 620 $aUS$dForestville$3UONL005852 676 $a133.44$cMagia amorosa$v21 700 1$aGårdbäck$bJohannes Björn$3UONV295567$01820976 712 $aThe *Ironwode Institution for the Preservation and Popularization of Indigenous Ethnomagicology (YIPPIE)$3UONV295568$4650 801 $aIT$bSOL$c20250711$gRICA 899 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$2UONSI 912 $aUON00524055 950 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$dSI STUDI NORD2024 003 $eSI 51199 5 003 951 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$bSI2024300 1J 20240416Bolla n. 159 del 10.5.2024. 996 $aTrolldom$94384215 997 $aUNIOR