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010   $a3-319-57914-2
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100   $a20170627d2017      u|         0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aGoldbach?s problem $eselected topics /$fby Michael Th. Rassias
205   $a1st ed. 2017.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017.
215   $a1 online resource (XV, 122 p.)
311   $a3-319-57912-6 
327   $aForeword -- 1. Introduction -- 2. Step by step proof of Vinogradov's theorem -- The ternary Goldbach problem with a prime and two isolated primes -- 4. Basic steps of the proof of Schnirelmann's theorem. - Appendix. - Index. -Bibliography.
330   $aImportant results surrounding the proof of Goldbach's ternary conjecture are presented in this book. Beginning with an historical perspective along with an overview of essential lemmas and theorems, this monograph moves on to a detailed proof of Vinogradov's theorem. The principles of the Hardy-Littlewood circle method are outlined and applied to Goldbach's ternary conjecture. New results due to H. Maier and the author on Vinogradov's theorem are proved under the assumption of the Riemann hypothesis. The final chapter discusses an approach to Goldbach's conjecture through theorems by L. G. Schnirelmann. This book concludes with an Appendix featuring a sketch of H. Helfgott's proof of Goldbach's ternary conjecture. The Appendix also presents some biographical remarks of mathematicians whose research has played a seminal role on the Goldbach ternary problem. The author's step-by-step approach makes this book accessible to those that have mastered classical number theory and fundamental notions of mathematical analysis. This book will be particularly useful to graduate students and mathematicians in analytic number theory, approximation theory as well as to researchers working on Goldbach's problem.
606   $aNumber theory
606   $aMathematical analysis
606   $aAnalysis (Mathematics)
606   $aNumerical analysis
606   $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001
606   $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007
606   $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050
615  0$aNumber theory.
615  0$aMathematical analysis.
615  0$aAnalysis (Mathematics).
615  0$aNumerical analysis.
615 14$aNumber Theory.
615 24$aAnalysis.
615 24$aNumerical Analysis.
676   $a512.7
700   $aRassias$b Michael Th$4aut$4http://id.loc.gov/vocabulary/relators/aut$0993670
906   $aBOOK
912   $a9910254273903321
996   $aGoldbach?s Problem$92275301
997   $aUNINA