Introduction to algebraic and Abelian functions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1982
|
| Edition: | 2. ed. |
| Series: | Graduate texts in mathematics
89 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 189 S. |
| ISBN: | 0387907106 3540907106 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV000229445 | ||
| 003 | DE-604 | ||
| 005 | 20141023 | ||
| 007 | t | ||
| 008 | 870612s1982 |||| 00||| eng d | ||
| 020 | |a 0387907106 |9 0-387-90710-6 | ||
| 020 | |a 3540907106 |9 3-540-90710-6 | ||
| 035 | |a (OCoLC)472091292 | ||
| 035 | |a (DE-599)BVBBV000229445 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-384 |a DE-703 |a DE-739 |a DE-355 |a DE-824 |a DE-19 |a DE-634 |a DE-83 |a DE-11 |a DE-188 | ||
| 084 | |a SK 240 |0 (DE-625)143226: |2 rvk | ||
| 084 | |a 14Fxx |2 msc | ||
| 084 | |a 14Kxx |2 msc | ||
| 084 | |a 14Hxx |2 msc | ||
| 084 | |a 14Jxx |2 msc | ||
| 100 | 1 | |a Lang, Serge |d 1927-2005 |e Verfasser |0 (DE-588)119305119 |4 aut | |
| 245 | 1 | 0 | |a Introduction to algebraic and Abelian functions |c Serge Lang |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 1982 | |
| 300 | |a IX, 189 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 89 | |
| 650 | 0 | 7 | |a Thetafunktion |0 (DE-588)4185175-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische Funktion |0 (DE-588)4141836-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Abelsche Funktion |0 (DE-588)4140987-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Algebraische Funktion |0 (DE-588)4141836-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Abelsche Funktion |0 (DE-588)4140987-5 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Thetafunktion |0 (DE-588)4185175-4 |D s |
| 689 | 2 | |5 DE-604 | |
| 689 | 3 | 0 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |D s |
| 689 | 3 | |8 1\p |5 DE-604 | |
| 830 | 0 | |a Graduate texts in mathematics |v 89 |w (DE-604)BV000000067 |9 89 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000137422&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 940 | 1 | |q TUB-www | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-000137422 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Record in the Search Index
| _version_ | 1804114692421976064 |
|---|---|
| adam_text | Contents
Chapter I
The Riemann Roch Theorem
§1. Lemmas on Valuations 1
§2. The Riemann Roch Theorem 5
§3. Remarks on Differential Forms 14
§4. Residues in Power Series Fields 16
§5. The Sum of the Residues 21
§6. The Genus Formula of Hurwitz 26
§7. Examples 27
§8. Differentials of Second Kind 29
§9. Function Fields and Curves 31
§10. Divisor Classes 34
Chapter II
The Fermat Curve
§1. The Genus 36
§2. Differentials 37
§3. Rational Images of the Fermat Curve 39
§4. Decomposition of the Divisor Classes 43
Chapter III
The Riemann Surface
§ 1. Topology and Analytic Structure 46
§2. Integration on the Riemann Surface 51
viii Contents
Chapter IV
The Theorem of Abel Jacobi
§ 1. Abelian Integrals 54
§2. Abel s Theorem 58
§3. Jacobi s Theorem 63
§4. Riemann s Relations 66
§5. Duality 67
Chapter V
Periods on the Fermat Curve
§ 1. The Logarithm Symbol 73
§2. Periods on the Universal Covering Space 75
§3. Periods on the Fermat Curve 77
§4. Periods on the Related Curves 81
Chapter VI
Linear Theory of Theta Functions
§ 1. Associated Linear Forms 83
§2. Degenerate Theta Functions 89
§3. Dimension of the Space of Theta Functions 90
§4. Abelian Functions and Riemann Roch Theorem on the Torus 97
§5. Translations of Theta Functions 101
§6. Projective Embedding 104
Chapter VII
Homomorphisms and Duality
§ 1. The Complex and Rational Representations 110
§2. Rational and p adic Representations 113
§3. Homomorphisms 116
§4. Complete Reducibility of Poincare 117
§5. The Dual Abelian Manifold 118
§6. Relations with Theta Functions 121
§7. The Kummer Pairing 124
§8. Periods and Homology 127
Chapter VIII
Riemann Matrices and Classical Theta Functions
§1. Riemann Matrices 131
§2. The Siegel Upper Half Space 135
§3. Fundamental Theta Functions 138
Contents ix
Chapter IX
Involutions and Abelian Manifolds of Quaternion Type
§ 1. Involutions 143
§2. Special Generators 146
§3. Orders 148
§4. Lattices and Riemann Forms on C2 Determined
by Quaternion Algebras 149
§5. Isomorphism Classes 154
Chapter X
Theta Functions and Divisors
§1. Positive Divisors 157
§2. Arbitrary Divisors 163
§3. Existence of a Riemann Form on an Abelian Variety 163
Bibliography 165
Index 167
|
| any_adam_object | 1 |
| author | Lang, Serge 1927-2005 |
| author_GND | (DE-588)119305119 |
| author_facet | Lang, Serge 1927-2005 |
| author_role | aut |
| author_sort | Lang, Serge 1927-2005 |
| author_variant | s l sl |
| building | Verbundindex |
| bvnumber | BV000229445 |
| classification_rvk | SK 240 |
| ctrlnum | (OCoLC)472091292 (DE-599)BVBBV000229445 |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02104nam a2200541 cb4500</leader><controlfield tag="001">BV000229445</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20141023 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">870612s1982 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387907106</subfield><subfield code="9">0-387-90710-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540907106</subfield><subfield code="9">3-540-90710-6</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)472091292</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV000229445</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 240</subfield><subfield code="0">(DE-625)143226:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">14Fxx</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">14Kxx</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">14Hxx</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">14Jxx</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Lang, Serge</subfield><subfield code="d">1927-2005</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)119305119</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Introduction to algebraic and Abelian functions</subfield><subfield code="c">Serge Lang</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">1982</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">IX, 189 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Graduate texts in mathematics</subfield><subfield code="v">89</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Thetafunktion</subfield><subfield code="0">(DE-588)4185175-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebraische Funktion</subfield><subfield code="0">(DE-588)4141836-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebraische Geometrie</subfield><subfield code="0">(DE-588)4001161-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Abelsche Funktion</subfield><subfield code="0">(DE-588)4140987-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Algebraische Funktion</subfield><subfield code="0">(DE-588)4141836-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Abelsche Funktion</subfield><subfield code="0">(DE-588)4140987-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Thetafunktion</subfield><subfield code="0">(DE-588)4185175-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="3" ind2="0"><subfield code="a">Algebraische Geometrie</subfield><subfield code="0">(DE-588)4001161-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="3" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Graduate texts in mathematics</subfield><subfield code="v">89</subfield><subfield code="w">(DE-604)BV000000067</subfield><subfield code="9">89</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000137422&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">TUB-www</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-000137422</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV000229445 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:10:45Z |
| institution | BVB |
| isbn | 0387907106 3540907106 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000137422 |
| oclc_num | 472091292 |
| open_access_boolean | |
| owner | DE-12 DE-384 DE-703 DE-739 DE-355 DE-BY-UBR DE-824 DE-19 DE-BY-UBM DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-12 DE-384 DE-703 DE-739 DE-355 DE-BY-UBR DE-824 DE-19 DE-BY-UBM DE-634 DE-83 DE-11 DE-188 |
| physical | IX, 189 S. |
| psigel | TUB-www |
| publishDate | 1982 |
| publishDateSearch | 1982 |
| publishDateSort | 1982 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Lang, Serge 1927-2005 Verfasser (DE-588)119305119 aut Introduction to algebraic and Abelian functions Serge Lang 2. ed. New York [u.a.] Springer 1982 IX, 189 S. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 89 Thetafunktion (DE-588)4185175-4 gnd rswk-swf Algebraische Funktion (DE-588)4141836-0 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Abelsche Funktion (DE-588)4140987-5 gnd rswk-swf Algebraische Funktion (DE-588)4141836-0 s DE-604 Abelsche Funktion (DE-588)4140987-5 s Thetafunktion (DE-588)4185175-4 s Algebraische Geometrie (DE-588)4001161-6 s 1\p DE-604 Graduate texts in mathematics 89 (DE-604)BV000000067 89 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000137422&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lang, Serge 1927-2005 Introduction to algebraic and Abelian functions Graduate texts in mathematics Thetafunktion (DE-588)4185175-4 gnd Algebraische Funktion (DE-588)4141836-0 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Abelsche Funktion (DE-588)4140987-5 gnd |
| subject_GND | (DE-588)4185175-4 (DE-588)4141836-0 (DE-588)4001161-6 (DE-588)4140987-5 |
| title | Introduction to algebraic and Abelian functions |
| title_auth | Introduction to algebraic and Abelian functions |
| title_exact_search | Introduction to algebraic and Abelian functions |
| title_full | Introduction to algebraic and Abelian functions Serge Lang |
| title_fullStr | Introduction to algebraic and Abelian functions Serge Lang |
| title_full_unstemmed | Introduction to algebraic and Abelian functions Serge Lang |
| title_short | Introduction to algebraic and Abelian functions |
| title_sort | introduction to algebraic and abelian functions |
| topic | Thetafunktion (DE-588)4185175-4 gnd Algebraische Funktion (DE-588)4141836-0 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Abelsche Funktion (DE-588)4140987-5 gnd |
| topic_facet | Thetafunktion Algebraische Funktion Algebraische Geometrie Abelsche Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000137422&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT langserge introductiontoalgebraicandabelianfunctions |