03669nam 22006855 450 991029999480332120231120142736.03-319-07545-410.1007/978-3-319-07545-7(CKB)3710000000143846(EBL)1783057(SSID)ssj0001274572(PQKBManifestationID)11749472(PQKBTitleCode)TC0001274572(PQKBWorkID)11325330(PQKB)11640307(DE-He213)978-3-319-07545-7(MiAaPQ)EBC6315515(MiAaPQ)EBC1783057(Au-PeEL)EBL1783057(CaPaEBR)ebr10976182(OCoLC)883022070(PPN)179767143(EXLCZ)99371000000014384620140623d2014 u| 0engur|n|---|||||txtccrAlgebraic Number Theory /by Frazer Jarvis1st ed. 2014.Cham :Springer International Publishing :Imprint: Springer,2014.1 online resource (298 p.)Springer Undergraduate Mathematics Series,1615-2085Description based upon print version of record.3-319-07544-6 Includes bibliographical references and index.Unique factorisation in the natural numbers -- Number fields -- Fields, discriminants and integral bases -- Ideals -- Prime ideals and unique factorisation -- Imaginary quadratic fields -- Lattices and geometrical methods -- Other fields of small degree -- Cyclotomic fields and the Fermat equation -- Analytic methods -- The number field sieve.The technical difficulties of algebraic number theory often make this subject appear difficult to beginners. This undergraduate textbook provides a welcome solution to these problems as it provides an approachable and thorough introduction to the topic. Algebraic Number Theory takes the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more general number fields often fail. Algebraic number theory aims to overcome this problem. Most examples are taken from quadratic fields, for which calculations are easy to perform. The middle section considers more general theory and results for number fields, and the book concludes with some topics which are more likely to be suitable for advanced students, namely, the analytic class number formula and the number field sieve. This is the first time that the number field sieve has been considered in a textbook at this level.Springer Undergraduate Mathematics Series,1615-2085Number theoryAlgebraField theory (Physics)Number Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M25001Field Theory and Polynomialshttps://scigraph.springernature.com/ontologies/product-market-codes/M11051Number theory.Algebra.Field theory (Physics).Number Theory.Field Theory and Polynomials.512.74Jarvis Frazerauthttp://id.loc.gov/vocabulary/relators/aut721290MiAaPQMiAaPQMiAaPQBOOK9910299994803321Algebraic number theory1410408UNINA