Modular forms on half-spaces of quaternions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin, [u.a.]
Springer
[1985]
|
| Series: | Lecture notes in mathematics
1143 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 203 Seiten |
| ISBN: | 3540156798 0387156798 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV000417811 | ||
| 003 | DE-604 | ||
| 005 | 20241014 | ||
| 007 | t | ||
| 008 | 870612s1985 |||| 00||| eng d | ||
| 020 | |a 3540156798 |9 3-540-15679-8 | ||
| 020 | |a 0387156798 |9 0-387-15679-8 | ||
| 035 | |a (OCoLC)230824288 | ||
| 035 | |a (DE-599)BVBBV000417811 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-91G |a DE-384 |a DE-355 |a DE-20 |a DE-824 |a DE-29T |a DE-19 |a DE-706 |a DE-11 |a DE-188 |a DE-83 | ||
| 084 | |a SI 850 |0 (DE-625)143199: |2 rvk | ||
| 084 | |a MAT 103f |2 stub | ||
| 084 | |a 10D20 |2 msc/1980 | ||
| 100 | 1 | |a Krieg, Aloys |d 1955- |0 (DE-588)140990577 |4 aut | |
| 245 | 1 | 0 | |a Modular forms on half-spaces of quaternions |c Aloys Krieg |
| 264 | 1 | |a Berlin, [u.a.] |b Springer |c [1985] | |
| 264 | 4 | |c © 1985 | |
| 300 | |a XII, 203 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1143 | |
| 650 | 0 | 7 | |a Quaternionenhalbraum |0 (DE-588)4176654-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Modulform |0 (DE-588)4128299-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Quaternionenschiefkörper |0 (DE-588)4176655-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Modulfunktion |0 (DE-588)4039855-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Quaternion |0 (DE-588)4176653-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Halbraum |0 (DE-588)4023001-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Modulform |0 (DE-588)4128299-1 |D s |
| 689 | 0 | 1 | |a Quaternionenhalbraum |0 (DE-588)4176654-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Quaternionenhalbraum |0 (DE-588)4176654-4 |D s |
| 689 | 1 | 1 | |a Modulfunktion |0 (DE-588)4039855-9 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Quaternion |0 (DE-588)4176653-2 |D s |
| 689 | 2 | 1 | |a Halbraum |0 (DE-588)4023001-6 |D s |
| 689 | 2 | 2 | |a Modulform |0 (DE-588)4128299-1 |D s |
| 689 | 2 | |5 DE-604 | |
| 689 | 3 | 0 | |a Modulform |0 (DE-588)4128299-1 |D s |
| 689 | 3 | 1 | |a Quaternionenschiefkörper |0 (DE-588)4176655-6 |D s |
| 689 | 3 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-540-39610-9 |
| 830 | 0 | |a Lecture notes in mathematics |v 1143 |w (DE-604)BV000676446 |9 1143 | |
| 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=000258092&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-000258092 | |
Record in the Search Index
| _version_ | 1812913259249926144 |
|---|---|
| adam_text |
Table of contents
Introduction V
Notations xiii
Chapter I Integral and Hermitian matrices 1
§1 Orderings 2
§2 Integral matrices 14
§3 Hermitian matrices 20
§4 MINKOWSKI's reduction theory 28
§5 Applications of reduction theory 37
Chapter II Modular group and fundamental domain 42
§1 Symplectic group and half space 43
§2 Modular group 54
§3 The fundamental domain F(n;F) 58
§4 Congruence subgroups 67
Chapter III Modular forms 71
§1 Analytic class invariants 72
§2 The vector space of modular forms 83
§3 Modular forms with respect to congruence
subgroups 92
§4 Relations between SIEGEL modular forms,
Hermitian modular forms and modular forms
of quaternions 96
Chapter IV Theta series 99
§1 Elementary properties of theta series 100
§2 Theta series as modular forms 110
§3 Theta series with respect to even quadratic
forms 117
§4 Singular modular forms 126
Chapter V EISENSTEIN and POINCARE series 136
§1 Integrals 137
§2 EISENSTEIN series 145
§3 POINCARE series 157
§4 Metrization 166
§5 Algebraical independence 174
IV
Chapter VI Modular functions 182
§1 The field of modular functions 183
§2 Modular functions with respect to congruence
subgroups and symmetric modular functions 189
§3 Relations between SIEGEL modular functions,
Hermitian modular functions and modular
functions of quaternions 102
Bibliography 196
List of symbols 200
Index 202 |
| any_adam_object | 1 |
| author | Krieg, Aloys 1955- |
| author_GND | (DE-588)140990577 |
| author_facet | Krieg, Aloys 1955- |
| author_role | aut |
| author_sort | Krieg, Aloys 1955- |
| author_variant | a k ak |
| building | Verbundindex |
| bvnumber | BV000417811 |
| classification_rvk | SI 850 |
| classification_tum | MAT 103f |
| ctrlnum | (OCoLC)230824288 (DE-599)BVBBV000417811 |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 cb4500</leader><controlfield tag="001">BV000417811</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20241014</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">870612s1985 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540156798</subfield><subfield code="9">3-540-15679-8</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387156798</subfield><subfield code="9">0-387-15679-8</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)230824288</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV000417811</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</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-91G</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-83</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 850</subfield><subfield code="0">(DE-625)143199:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 103f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">10D20</subfield><subfield code="2">msc/1980</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Krieg, Aloys</subfield><subfield code="d">1955-</subfield><subfield code="0">(DE-588)140990577</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Modular forms on half-spaces of quaternions</subfield><subfield code="c">Aloys Krieg</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin, [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">[1985]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 1985</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XII, 203 Seiten</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">Lecture notes in mathematics</subfield><subfield code="v">1143</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Quaternionenhalbraum</subfield><subfield code="0">(DE-588)4176654-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Modulform</subfield><subfield code="0">(DE-588)4128299-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Quaternionenschiefkörper</subfield><subfield code="0">(DE-588)4176655-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Modulfunktion</subfield><subfield code="0">(DE-588)4039855-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Quaternion</subfield><subfield code="0">(DE-588)4176653-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Halbraum</subfield><subfield code="0">(DE-588)4023001-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Modulform</subfield><subfield code="0">(DE-588)4128299-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Quaternionenhalbraum</subfield><subfield code="0">(DE-588)4176654-4</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">Quaternionenhalbraum</subfield><subfield code="0">(DE-588)4176654-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Modulfunktion</subfield><subfield code="0">(DE-588)4039855-9</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">Quaternion</subfield><subfield code="0">(DE-588)4176653-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2="1"><subfield code="a">Halbraum</subfield><subfield code="0">(DE-588)4023001-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2="2"><subfield code="a">Modulform</subfield><subfield code="0">(DE-588)4128299-1</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">Modulform</subfield><subfield code="0">(DE-588)4128299-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="3" ind2="1"><subfield code="a">Quaternionenschiefkörper</subfield><subfield code="0">(DE-588)4176655-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="3" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-3-540-39610-9</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Lecture notes in mathematics</subfield><subfield code="v">1143</subfield><subfield code="w">(DE-604)BV000676446</subfield><subfield code="9">1143</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=000258092&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-000258092</subfield></datafield></record></collection> |
| id | DE-604.BV000417811 |
| illustrated | Not Illustrated |
| indexdate | 2024-10-14T18:00:13Z |
| institution | BVB |
| isbn | 3540156798 0387156798 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000258092 |
| oclc_num | 230824288 |
| open_access_boolean | |
| owner | DE-12 DE-91G DE-BY-TUM DE-384 DE-355 DE-BY-UBR DE-20 DE-824 DE-29T DE-19 DE-BY-UBM DE-706 DE-11 DE-188 DE-83 |
| owner_facet | DE-12 DE-91G DE-BY-TUM DE-384 DE-355 DE-BY-UBR DE-20 DE-824 DE-29T DE-19 DE-BY-UBM DE-706 DE-11 DE-188 DE-83 |
| physical | XII, 203 Seiten |
| psigel | TUB-nve |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Krieg, Aloys 1955- (DE-588)140990577 aut Modular forms on half-spaces of quaternions Aloys Krieg Berlin, [u.a.] Springer [1985] © 1985 XII, 203 Seiten txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1143 Quaternionenhalbraum (DE-588)4176654-4 gnd rswk-swf Modulform (DE-588)4128299-1 gnd rswk-swf Quaternionenschiefkörper (DE-588)4176655-6 gnd rswk-swf Modulfunktion (DE-588)4039855-9 gnd rswk-swf Quaternion (DE-588)4176653-2 gnd rswk-swf Halbraum (DE-588)4023001-6 gnd rswk-swf Modulform (DE-588)4128299-1 s Quaternionenhalbraum (DE-588)4176654-4 s DE-604 Modulfunktion (DE-588)4039855-9 s Quaternion (DE-588)4176653-2 s Halbraum (DE-588)4023001-6 s Quaternionenschiefkörper (DE-588)4176655-6 s Erscheint auch als Online-Ausgabe 978-3-540-39610-9 Lecture notes in mathematics 1143 (DE-604)BV000676446 1143 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000258092&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Krieg, Aloys 1955- Modular forms on half-spaces of quaternions Lecture notes in mathematics Quaternionenhalbraum (DE-588)4176654-4 gnd Modulform (DE-588)4128299-1 gnd Quaternionenschiefkörper (DE-588)4176655-6 gnd Modulfunktion (DE-588)4039855-9 gnd Quaternion (DE-588)4176653-2 gnd Halbraum (DE-588)4023001-6 gnd |
| subject_GND | (DE-588)4176654-4 (DE-588)4128299-1 (DE-588)4176655-6 (DE-588)4039855-9 (DE-588)4176653-2 (DE-588)4023001-6 |
| title | Modular forms on half-spaces of quaternions |
| title_auth | Modular forms on half-spaces of quaternions |
| title_exact_search | Modular forms on half-spaces of quaternions |
| title_full | Modular forms on half-spaces of quaternions Aloys Krieg |
| title_fullStr | Modular forms on half-spaces of quaternions Aloys Krieg |
| title_full_unstemmed | Modular forms on half-spaces of quaternions Aloys Krieg |
| title_short | Modular forms on half-spaces of quaternions |
| title_sort | modular forms on half spaces of quaternions |
| topic | Quaternionenhalbraum (DE-588)4176654-4 gnd Modulform (DE-588)4128299-1 gnd Quaternionenschiefkörper (DE-588)4176655-6 gnd Modulfunktion (DE-588)4039855-9 gnd Quaternion (DE-588)4176653-2 gnd Halbraum (DE-588)4023001-6 gnd |
| topic_facet | Quaternionenhalbraum Modulform Quaternionenschiefkörper Modulfunktion Quaternion Halbraum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000258092&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT kriegaloys modularformsonhalfspacesofquaternions |