LEADER 03669nam 22006855 450 001 9910299994803321 005 20231120142736.0 010 $a3-319-07545-4 024 7 $a10.1007/978-3-319-07545-7 035 $a(CKB)3710000000143846 035 $a(EBL)1783057 035 $a(SSID)ssj0001274572 035 $a(PQKBManifestationID)11749472 035 $a(PQKBTitleCode)TC0001274572 035 $a(PQKBWorkID)11325330 035 $a(PQKB)11640307 035 $a(DE-He213)978-3-319-07545-7 035 $a(MiAaPQ)EBC6315515 035 $a(MiAaPQ)EBC1783057 035 $a(Au-PeEL)EBL1783057 035 $a(CaPaEBR)ebr10976182 035 $a(OCoLC)883022070 035 $a(PPN)179767143 035 $a(EXLCZ)993710000000143846 100 $a20140623d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAlgebraic Number Theory /$fby Frazer Jarvis 205 $a1st ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014. 215 $a1 online resource (298 p.) 225 1 $aSpringer Undergraduate Mathematics Series,$x1615-2085 300 $aDescription based upon print version of record. 311 $a3-319-07544-6 320 $aIncludes bibliographical references and index. 327 $aUnique 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. 330 $aThe technical difficulties of algebraic number theory often make this subject appear difficult to beginners. This undergraduate textbook provides a welcome solution to these problems as it provides an approachable and thorough introduction to the topic. Algebraic Number Theory takes the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more general number fields often fail. Algebraic number theory aims to overcome this problem. Most examples are taken from quadratic fields, for which calculations are easy to perform. The middle section considers more general theory and results for number fields, and the book concludes with some topics which are more likely to be suitable for advanced students, namely, the analytic class number formula and the number field sieve. This is the first time that the number field sieve has been considered in a textbook at this level. 410 0$aSpringer Undergraduate Mathematics Series,$x1615-2085 606 $aNumber theory 606 $aAlgebra 606 $aField theory (Physics) 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 606 $aField Theory and Polynomials$3https://scigraph.springernature.com/ontologies/product-market-codes/M11051 615 0$aNumber theory. 615 0$aAlgebra. 615 0$aField theory (Physics). 615 14$aNumber Theory. 615 24$aField Theory and Polynomials. 676 $a512.74 700 $aJarvis$b Frazer$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721290 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299994803321 996 $aAlgebraic number theory$91410408 997 $aUNINA