An invitation to algebraic numbers and algebraic functions / (Record no. 71266)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 04163cam a2200553Ii 4500 |
| 001 - CONTROL NUMBER | |
| control field | 9780429506550 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20220711212429.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 200512s2020 flu ob 001 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9780429506550 |
| -- | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 0429506554 |
| -- | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9780429014666 |
| -- | (electronic bk. : EPUB) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 042901466X |
| -- | (electronic bk. : EPUB) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9780429014673 |
| -- | (electronic bk. : PDF) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 0429014678 |
| -- | (electronic bk. : PDF) |
| 082 04 - CLASSIFICATION NUMBER | |
| Call Number | 512.7/4 |
| 100 1# - AUTHOR NAME | |
| Author | Halter-Koch, Franz, |
| 245 13 - TITLE STATEMENT | |
| Title | An invitation to algebraic numbers and algebraic functions / |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | 1 online resource (xiv, 580 pages) |
| 500 ## - GENERAL NOTE | |
| Remark 1 | "A Chapman & Hall book." |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | 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). |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Remark 2 | 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 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | https://www.taylorfrancis.com/books/9780429506550 |
| 856 42 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | http://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | eBooks |
| 264 #1 - | |
| -- | Boca Raton : |
| -- | CRC Press, Taylor & Francis Group, |
| -- | 2020. |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 588 ## - | |
| -- | OCLC-licensed vendor bibliographic record. |
| 650 #7 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | MATHEMATICS / General |
| 650 #7 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | MATHEMATICS / Algebra / General |
| 650 #7 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | MATHEMATICS / Number Theory |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Algebraic fields. |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Algebraic functions. |
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