LEADER 04118nam 22006975 450 001 9910299989203321 005 20220302151213.0 010 $a1-4939-0832-4 024 7 $a10.1007/978-1-4939-0832-5 035 $a(CKB)3710000000143774 035 $a(EBL)1782034 035 $a(SSID)ssj0001278174 035 $a(PQKBManifestationID)11951373 035 $a(PQKBTitleCode)TC0001278174 035 $a(PQKBWorkID)11279830 035 $a(PQKB)10465161 035 $a(DE-He213)978-1-4939-0832-5 035 $a(MiAaPQ)EBC6311427 035 $a(MiAaPQ)EBC1782034 035 $a(Au-PeEL)EBL1782034 035 $a(CaPaEBR)ebr10969072 035 $a(OCoLC)882553933 035 $a(PPN)179763369 035 $a(EXLCZ)993710000000143774 100 $a20140624d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aTranscendental Numbers /$fby M. Ram Murty, Purusottam Rath 205 $a1st ed. 2014. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2014. 215 $a1 online resource (219 p.) 300 $aDescription based upon print version of record. 311 0 $a1-4939-0831-6 320 $aIncludes bibliographical references (pages [205]-213) and index. 327 $a1. 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).      . 330 $aThis 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. 606 $aNumber theory 606 $aAlgebra 606 $aMathematical analysis 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 606 $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 615 0$aNumber theory. 615 0$aAlgebra. 615 0$aMathematical analysis. 615 14$aNumber Theory. 615 24$aAlgebra. 615 24$aAnalysis. 676 $a512.73 700 $aMurty$b M. Ram$4aut$4http://id.loc.gov/vocabulary/relators/aut$061548 702 $aRath$b Purusottam$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299989203321 996 $aTranscendental Numbers$92541508 997 $aUNINA