Rational points on elliptic curves:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cham [u.a.]
Springer
2015
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Undergraduate texts in mathematics
|
| Schlagworte: | |
| Online-Zugang: | BTU01 FRO01 TUM01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Beschreibung: | 1 Online-Ressource (XXII, 332 S.) 37 illus |
| ISBN: | 9783319185880 |
| ISSN: | 0172-6056 |
| DOI: | 10.1007/978-3-319-18588-0 |
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Datensatz im Suchindex
| _version_ | 1804174858913841153 |
|---|---|
| adam_text | RATIONAL POINTS ON ELLIPTIC CURVES
/ SILVERMAN, JOSEPH H.
: 2015
TABLE OF CONTENTS / INHALTSVERZEICHNIS
INTRODUCTION
GEOMETRY AND ARITHMETIC
POINTS OF FINITE ORDER
THE GROUP OF RATIONAL POINTS
CUBIC CURVES OVER FINITE FIELDS
INTEGER POINTS ON CUBIC CURVES
COMPLEX MULTIPLICATION
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
RATIONAL POINTS ON ELLIPTIC CURVES
/ SILVERMAN, JOSEPH H.
: 2015
ABSTRACT / INHALTSTEXT
THE THEORY OF ELLIPTIC CURVES INVOLVES A PLEASING BLEND OF ALGEBRA,
GEOMETRY, ANALYSIS, AND NUMBER THEORY. THIS BOOK STRESSES THIS INTERPLAY
AS IT DEVELOPS THE BASIC THEORY, THEREBY PROVIDING AN OPPORTUNITY FOR
ADVANCED UNDERGRADUATES TO APPRECIATE THE UNITY OF MODERN MATHEMATICS.
AT THE SAME TIME, EVERY EFFORT HAS BEEN MADE TO USE ONLY METHODS AND
RESULTS COMMONLY INCLUDED IN THE UNDERGRADUATE CURRICULUM. THIS
ACCESSIBILITY, THE INFORMAL WRITING STYLE, AND A WEALTH OF EXERCISES
MAKE RATIONAL POINTS ON ELLIPTIC CURVES AN IDEAL INTRODUCTION FOR
STUDENTS AT ALL LEVELS WHO ARE INTERESTED IN LEARNING ABOUT DIOPHANTINE
EQUATIONS AND ARITHMETIC GEOMETRY. MOST CONCRETELY, AN ELLIPTIC CURVE IS
THE SET OF ZEROES OF A CUBIC POLYNOMIAL IN TWO VARIABLES. IF THE
POLYNOMIAL HAS RATIONAL COEFFICIENTS, THEN ONE CAN ASK FOR A DESCRIPTION
OF THOSE ZEROES WHOSE COORDINATES ARE EITHER INTEGERS OR RATIONAL
NUMBERS. IT IS THIS NUMBER THEORETIC QUESTION THAT IS THE MAIN SUBJECT
OF THIS BOOK. TOPICS COVERED INCLUDE THE GEOMETRY AND GROUP STRUCTURE OF
ELLIPTIC CURVES, THE NAGELL–LUTZ THEOREM DESCRIBING POINTS OF FINITE
ORDER, THE MORDELL–WEIL THEOREM ON THE FINITE GENERATION OF THE GROUP
OF RATIONAL POINTS, THE THUE–SIEGEL THEOREM ON THE FINITENESS OF THE
SET OF INTEGER POINTS, THEOREMS ON COUNTING POINTS WITH COORDINATES IN
FINITE FIELDS, LENSTRA’S ELLIPTIC CURVE FACTORIZATION ALGORITHM, AND A
DISCUSSION OF COMPLEX MULTIPLICATION AND THE GALOIS REPRESENTATIONS
ASSOCIATED TO TORSION POINTS. ADDITIONAL TOPICS NEW TO THE SECOND
EDITION INCLUDE AN INTRODUCTION TO ELLIPTIC CURVE CRYPTOGRAPHY AND A
BRIEF DISCUSSION OF THE STUNNING PROOF OF FERMAT’S LAST THEOREM BY
WILES ET AL. VIA THE USE OF ELLIPTIC CURVES
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Silverman, Joseph H. 1955- |
| author_GND | (DE-588)118906933 (DE-588)117726079 |
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| author_sort | Silverman, Joseph H. 1955- |
| author_variant | j h s jh jhs |
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| dewey-sort | 3516.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-319-18588-0 |
| edition | 2. ed. |
| format | Electronic eBook |
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| issn | 0172-6056 |
| language | English |
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| series2 | Undergraduate texts in mathematics |
| spelling | Silverman, Joseph H. 1955- Verfasser (DE-588)118906933 aut Rational points on elliptic curves Joseph H. Silverman ; John T. Tate 2. ed. Cham [u.a.] Springer 2015 1 Online-Ressource (XXII, 332 S.) 37 illus txt rdacontent c rdamedia cr rdacarrier Undergraduate texts in mathematics 0172-6056 Mathematics Data structures (Computer science) Geometry, algebraic Number theory Algebraic Geometry Number Theory Data Structures, Cryptology and Information Theory Mathematik Diophantische Analysis (DE-588)4150020-9 gnd rswk-swf Algebraische Kurve (DE-588)4001165-3 gnd rswk-swf Elliptische Kurve (DE-588)4014487-2 gnd rswk-swf Rationaler Punkt (DE-588)4177004-3 gnd rswk-swf Rationaler Punkt (DE-588)4177004-3 s Elliptische Kurve (DE-588)4014487-2 s DE-604 Algebraische Kurve (DE-588)4001165-3 s Diophantische Analysis (DE-588)4150020-9 s Tate, John Torrence 1925-2019 Sonstige (DE-588)117726079 oth Erscheint auch als Druckausgabe 978-3-319-18587-3 https://doi.org/10.1007/978-3-319-18588-0 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028101536&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028101536&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Silverman, Joseph H. 1955- Rational points on elliptic curves Mathematics Data structures (Computer science) Geometry, algebraic Number theory Algebraic Geometry Number Theory Data Structures, Cryptology and Information Theory Mathematik Diophantische Analysis (DE-588)4150020-9 gnd Algebraische Kurve (DE-588)4001165-3 gnd Elliptische Kurve (DE-588)4014487-2 gnd Rationaler Punkt (DE-588)4177004-3 gnd |
| subject_GND | (DE-588)4150020-9 (DE-588)4001165-3 (DE-588)4014487-2 (DE-588)4177004-3 |
| title | Rational points on elliptic curves |
| title_auth | Rational points on elliptic curves |
| title_exact_search | Rational points on elliptic curves |
| title_full | Rational points on elliptic curves Joseph H. Silverman ; John T. Tate |
| title_fullStr | Rational points on elliptic curves Joseph H. Silverman ; John T. Tate |
| title_full_unstemmed | Rational points on elliptic curves Joseph H. Silverman ; John T. Tate |
| title_short | Rational points on elliptic curves |
| title_sort | rational points on elliptic curves |
| topic | Mathematics Data structures (Computer science) Geometry, algebraic Number theory Algebraic Geometry Number Theory Data Structures, Cryptology and Information Theory Mathematik Diophantische Analysis (DE-588)4150020-9 gnd Algebraische Kurve (DE-588)4001165-3 gnd Elliptische Kurve (DE-588)4014487-2 gnd Rationaler Punkt (DE-588)4177004-3 gnd |
| topic_facet | Mathematics Data structures (Computer science) Geometry, algebraic Number theory Algebraic Geometry Number Theory Data Structures, Cryptology and Information Theory Mathematik Diophantische Analysis Algebraische Kurve Elliptische Kurve Rationaler Punkt |
| url | https://doi.org/10.1007/978-3-319-18588-0 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028101536&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028101536&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT silvermanjosephh rationalpointsonellipticcurves AT tatejohntorrence rationalpointsonellipticcurves |