04118nam 22006975 450 991029998920332120220302151213.01-4939-0832-410.1007/978-1-4939-0832-5(CKB)3710000000143774(EBL)1782034(SSID)ssj0001278174(PQKBManifestationID)11951373(PQKBTitleCode)TC0001278174(PQKBWorkID)11279830(PQKB)10465161(DE-He213)978-1-4939-0832-5(MiAaPQ)EBC6311427(MiAaPQ)EBC1782034(Au-PeEL)EBL1782034(CaPaEBR)ebr10969072(OCoLC)882553933(PPN)179763369(EXLCZ)99371000000014377420140624d2014 u| 0engur|n|---|||||txtccrTranscendental Numbers /by M. Ram Murty, Purusottam Rath1st ed. 2014.New York, NY :Springer New York :Imprint: Springer,2014.1 online resource (219 p.)Description based upon print version of record.1-4939-0831-6 Includes bibliographical references (pages [205]-213) and index.1. Liouville’s theorem -- 2. Hermite’s Theorem -- 3. Lindemann’s theorem -- 4. The Lindemann-Weierstrass theorem -- 5. The maximum modulus principle -- 6. Siegel’s lemma -- 7. The six exponentials theorem -- 8. Estimates for derivatives -- 9. The Schneider-Lang theorem -- 10. Elliptic functions -- 11. Transcendental values of elliptic functions -- 12. Periods and quasiperiods -- 13. Transcendental values of some elliptic integrals -- 14. The modular invariant -- 15. Transcendental values of the j-function -- 16. More elliptic integrals -- 17. Transcendental values of Eisenstein series -- 18. Elliptic integrals and hypergeometric series -- 19. Baker’s theorem -- 20. Some applications of Baker’s theorem -- 21. Schanuel’s conjecture -- 22. Transcendental values of some Dirichlet series -- 23. Proof of the Baker-Birch-Wirsing theorem -- 24. Transcendence of some infinite series -- 25. Linear independence of values of Dirichlet L-functions -- 26. Transcendence of values of modular forms -- 27. Transcendence of values of class group L-functions -- 28. Periods, multiple zeta functions and (3).      .This book provides an introduction to the topic of transcendental numbers for upper-level undergraduate and graduate students. The text is constructed to support a full course on the subject, including descriptions of both relevant theorems and their applications. While the first part of the book focuses on introducing key concepts, the second part presents more complex material, including applications of Baker’s theorem, Schanuel’s conjecture, and Schneider’s theorem. These later chapters may be of interest to researchers interested in examining the relationship between transcendence and L-functions. Readers of this text should possess basic knowledge of complex analysis and elementary algebraic number theory.Number theoryAlgebraMathematical analysisNumber Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M25001Algebrahttps://scigraph.springernature.com/ontologies/product-market-codes/M11000Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12007Number theory.Algebra.Mathematical analysis.Number Theory.Algebra.Analysis.512.73Murty M. Ramauthttp://id.loc.gov/vocabulary/relators/aut61548Rath Purusottamauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910299989203321Transcendental Numbers2541508UNINA00952nam0-2200289 --450 991100198610332120250522091048.020250522d1892----kmuy0itay5050 baitaITa 001yyFibre tessili, filati, tessuti e carte di varia natura e variamente coloratiCarlo Aurelio RevelliMilanoDumolard1892XVI, 445 p.ill.19 cm.Alterazione e falsificazione delle sostanze alimentari e di altre importanti materie ad uso comuneTessutiFilatiCarta67723itaRevelli,Carlo Aurelio1359997ITUNINAREICATUNIMARCBK9911001986103321A MUSA 37303/3161/25FAGBCFAGBCFibre tessili, filati, tessuti e carte di varia natura e variamente colorati4380031UNINA