UID:
almahu_9949386092202882
Umfang:
1 online resource (xiv, 580 pages)
ISBN:
9780429506550
,
0429506554
,
9780429014666
,
042901466X
,
9780429014673
,
0429014678
,
9780429014659
,
0429014651
Inhalt:
The 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)
Anmerkung:
"A Chapman & Hall book."
,
1 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
Weitere Ausg.:
Print version: Halter-Koch, Franz, 1944- Invitation to algebraic numbers and algebraic functions. Boca Raton : CRC Press, Taylor & Francis Group, 2020 ISBN 1138583588
Weitere Ausg.:
ISBN 9781138583580
Sprache:
Englisch
Schlagwort(e):
Electronic books.
;
Electronic books.
URL:
https://www.taylorfrancis.com/books/9780429506550
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