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001 9780429506550
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008 200512s2020 flu ob 001 0 eng d
040 _aOCoLC-P
_beng
_erda
_epn
_cOCoLC-P
020 _a9780429506550
_q(electronic bk.)
020 _a0429506554
_q(electronic bk.)
020 _a9780429014666
_q(electronic bk. : EPUB)
020 _a042901466X
_q(electronic bk. : EPUB)
020 _z9781138583610
020 _a9780429014673
_q(electronic bk. : PDF)
020 _a0429014678
_q(electronic bk. : PDF)
020 _z1138583588
020 _z9781138583580
035 _a(OCoLC)1154016889
_z(OCoLC)1153453960
035 _a(OCoLC-P)1154016889
050 4 _aQA247
072 7 _aMAT
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_2bisacsh
072 7 _aMAT
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072 7 _aMAT
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072 7 _aPBF
_2bicssc
082 0 4 _a512.7/4
_223
100 1 _aHalter-Koch, Franz,
_d1944-
_eauthor.
_916483
245 1 3 _aAn invitation to algebraic numbers and algebraic functions /
_cFranz Halter-Koch, University of Graz, Austria.
264 1 _aBoca Raton :
_bCRC Press, Taylor & Francis Group,
_c2020.
300 _a1 online resource (xiv, 580 pages)
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
500 _a"A Chapman & Hall book."
520 _aThe author offers a thorough presentation of the classical theory of algebraic numbers and algebraic functions which both in its conception and in many details differs from the current literature on the subject. The basic features are: Field-theoretic preliminaries and a detailed presentation of Dedekind's ideal theory including non-principal orders and various types of class groups; the classical theory of algebraic number fields with a focus on quadratic, cubic and cyclotomic fields; basics of the analytic theory including the prime ideal theorem, density results and the determination of the arithmetic by the class group; a thorough presentation of valuation theory including the theory of difference, discriminants, and higher ramification. The theory of function fields is based on the ideal and valuation theory developed before; it presents the Riemann-Roch theorem on the basis of Weil differentials and highlights in detail the connection with classical differentials. The theory of congruence zeta functions and a proof of the Hasse-Weil theorem represent the culminating point of the volume. The volume is accessible with a basic knowledge in algebra and elementary number theory. It empowers the reader to follow the advanced number-theoretic literature, and is a solid basis for the study of the forthcoming volume on the foundations and main results of class field theory. Key features: " A thorough presentation of the theory of Algebraic Numbers and Algebraic Functions on an ideal and valuation-theoretic basis. " Several of the topics both in the number field and in the function field case were not presented before in this context. " Despite presenting many advanced topics, the text is easily readable. Franz Halter-Koch is professor emeritus at the university of Graz. He is the author of "Ideal Systems" (Marcel Dekker,1998), "Quadratic Irrationals" (CRC, 2013), and a co-author of "Non-Unique Factorizations" (CRC 2006).
505 0 _a1 Field Extensions 2 Dedekind Theory 3 Algebraic Number Fields: Elementary and Geometric Methods 4 Elementary Analytic Theory 5 Valuation Theory 6 Algebraic Function Fields Bibliography Index List of Symbols
588 _aOCLC-licensed vendor bibliographic record.
650 7 _aMATHEMATICS / General
_2bisacsh
_916484
650 7 _aMATHEMATICS / Algebra / General
_2bisacsh
_913209
650 7 _aMATHEMATICS / Number Theory
_2bisacsh
_915665
650 0 _aAlgebraic fields.
_916485
650 0 _aAlgebraic functions.
_916486
856 4 0 _3Taylor & Francis
_uhttps://www.taylorfrancis.com/books/9780429506550
856 4 2 _3OCLC metadata license agreement
_uhttp://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf
942 _cEBK
999 _c71266
_d71266