LEADER 03215nam 22005055 450 001 996418270803316 005 20231016163447.0 010 $a981-15-4155-8 024 7 $a10.1007/978-981-15-4155-1 035 $a(CKB)4100000011242017 035 $a(DE-He213)978-981-15-4155-1 035 $a(MiAaPQ)EBC6190194 035 $a(PPN)248393561 035 $a(EXLCZ)994100000011242017 100 $a20200502d2020 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aPillars of Transcendental Number Theory$b[electronic resource] /$fby Saradha Natarajan, Ravindranathan Thangadurai 205 $a1st ed. 2020. 210 1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2020. 215 $a1 online resource (XVII, 174 p. 27 illus., 2 illus. in color.) 311 $a981-15-4154-X 327 $a1. Preliminaries -- 2. e and pi are Transcendental -- 3. Theorem of Hermite-Lindemann-Weierstrass -- 4. Theorem of Gelfond and Schneider -- 5. Extensions due to Ramachandra -- 6. Diophantine Approximation and Transcendence -- 7. Roth's Theorem -- 8. Baker's Theorems and some Applications -- 9. Ground Work for the Proof of Baker's theorem -- 10. Proof of Baker's Theorem -- 11. Subspace Theorem and Some Applications. 330 $aThis book deals with the development of Diophantine problems starting with Thue's path breaking result and culminating in Roth's theorem with applications. It discusses classical results including Hermite?Lindemann?Weierstrass theorem, Gelfond?Schneider theorem, Schmidt?s subspace theorem and more. It also includes two theorems of Ramachandra which are not widely known and other interesting results derived on the values of Weierstrass elliptic function. Given the constantly growing number of applications of linear forms in logarithms, it is becoming increasingly important for any student wanting to work in this area to know the proofs of Baker?s original results. This book presents Baker?s original results in a format suitable for graduate students, with a focus on presenting the content in an accessible and simple manner. Each student-friendly chapter concludes with selected problems in the form of ?Exercises? and interesting information presented as ?Notes,? intended to spark readers? curiosity. 606 $aNumber theory 606 $aFunctions of real variables 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 606 $aReal Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12171 615 0$aNumber theory. 615 0$aFunctions of real variables. 615 14$aNumber Theory. 615 24$aReal Functions. 676 $a512.7 700 $aNatarajan$b Saradha$4aut$4http://id.loc.gov/vocabulary/relators/aut$01017961 702 $aThangadurai$b Ravindranathan$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418270803316 996 $aPillars of Transcendental Number Theory$92391158 997 $aUNISA