Generalized Analytic Automorphic Forms in Hypercomplex Spaces:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
2004
|
| Schriftenreihe: | Frontiers in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book describes the basic theory of hypercomplex-analytic automorphic forms and functions for arithmetic subgroups of the Vahlen group in higher dimensional spaces. Hypercomplex analyticity generalizes the concept of complex analyticity in the sense of considering null-solutions to higher dimensional Cauchy-Riemann type systems. Vector- and Clifford algebra-valued Eisenstein and Poincaré series are constructed within this framework and a detailed description of their analytic and number theoretical properties is provided. In particular, explicit relationships to generalized variants of the Riemann zeta function and Dirichlet L-series are established and a concept of hypercomplex multiplication of lattices is introduced. Applications to the theory of Hilbert spaces with reproducing kernels, to partial differential equations and index theory on some conformal manifolds are also described |
| Beschreibung: | 1 Online-Ressource (XV, 168 p) |
| ISBN: | 9783764378042 9783764370596 |
| ISSN: | 1660-8046 |
| DOI: | 10.1007/b95203 |
Internformat
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV042423585 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s2004 |||| o||u| ||||||eng d | ||
| 020 | |a 9783764378042 |c Online |9 978-3-7643-7804-2 | ||
| 020 | |a 9783764370596 |c Print |9 978-3-7643-7059-6 | ||
| 024 | 7 | |a 10.1007/b95203 |2 doi | |
| 035 | |a (OCoLC)837759527 | ||
| 035 | |a (DE-599)BVBBV042423585 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 515.5 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Krausshar, Rolf Sören |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Generalized Analytic Automorphic Forms in Hypercomplex Spaces |c by Rolf Sören Krausshar |
| 264 | 1 | |a Basel |b Birkhäuser Basel |c 2004 | |
| 300 | |a 1 Online-Ressource (XV, 168 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Frontiers in Mathematics |x 1660-8046 | |
| 500 | |a This book describes the basic theory of hypercomplex-analytic automorphic forms and functions for arithmetic subgroups of the Vahlen group in higher dimensional spaces. Hypercomplex analyticity generalizes the concept of complex analyticity in the sense of considering null-solutions to higher dimensional Cauchy-Riemann type systems. Vector- and Clifford algebra-valued Eisenstein and Poincaré series are constructed within this framework and a detailed description of their analytic and number theoretical properties is provided. In particular, explicit relationships to generalized variants of the Riemann zeta function and Dirichlet L-series are established and a concept of hypercomplex multiplication of lattices is introduced. Applications to the theory of Hilbert spaces with reproducing kernels, to partial differential equations and index theory on some conformal manifolds are also described | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Integral Transforms | |
| 650 | 4 | |a Potential theory (Mathematics) | |
| 650 | 4 | |a Sequences (Mathematics) | |
| 650 | 4 | |a Functions, special | |
| 650 | 4 | |a Number theory | |
| 650 | 4 | |a Special Functions | |
| 650 | 4 | |a Integral Transforms, Operational Calculus | |
| 650 | 4 | |a Potential Theory | |
| 650 | 4 | |a Sequences, Series, Summability | |
| 650 | 4 | |a Number Theory | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Automorphe Form |0 (DE-588)4003972-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Hardy-Raum |0 (DE-588)4159109-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Automorphe Form |0 (DE-588)4003972-9 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Hardy-Raum |0 (DE-588)4159109-4 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/b95203 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027859002 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153099507466240 |
|---|---|
| any_adam_object | |
| author | Krausshar, Rolf Sören |
| author_facet | Krausshar, Rolf Sören |
| author_role | aut |
| author_sort | Krausshar, Rolf Sören |
| author_variant | r s k rs rsk |
| building | Verbundindex |
| bvnumber | BV042423585 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)837759527 (DE-599)BVBBV042423585 |
| dewey-full | 515.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.5 |
| dewey-search | 515.5 |
| dewey-sort | 3515.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/b95203 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02963nmm a2200601zc 4500</leader><controlfield tag="001">BV042423585</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s2004 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783764378042</subfield><subfield code="c">Online</subfield><subfield code="9">978-3-7643-7804-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783764370596</subfield><subfield code="c">Print</subfield><subfield code="9">978-3-7643-7059-6</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/b95203</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)837759527</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042423585</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.5</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Krausshar, Rolf Sören</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Generalized Analytic Automorphic Forms in Hypercomplex Spaces</subfield><subfield code="c">by Rolf Sören Krausshar</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Basel</subfield><subfield code="b">Birkhäuser Basel</subfield><subfield code="c">2004</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XV, 168 p)</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">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Frontiers in Mathematics</subfield><subfield code="x">1660-8046</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">This book describes the basic theory of hypercomplex-analytic automorphic forms and functions for arithmetic subgroups of the Vahlen group in higher dimensional spaces. Hypercomplex analyticity generalizes the concept of complex analyticity in the sense of considering null-solutions to higher dimensional Cauchy-Riemann type systems. Vector- and Clifford algebra-valued Eisenstein and Poincaré series are constructed within this framework and a detailed description of their analytic and number theoretical properties is provided. In particular, explicit relationships to generalized variants of the Riemann zeta function and Dirichlet L-series are established and a concept of hypercomplex multiplication of lattices is introduced. Applications to the theory of Hilbert spaces with reproducing kernels, to partial differential equations and index theory on some conformal manifolds are also described</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Integral Transforms</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Potential theory (Mathematics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Sequences (Mathematics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functions, special</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Number theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Special Functions</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Integral Transforms, Operational Calculus</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Potential Theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Sequences, Series, Summability</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Number Theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Automorphe Form</subfield><subfield code="0">(DE-588)4003972-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Hardy-Raum</subfield><subfield code="0">(DE-588)4159109-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Automorphe Form</subfield><subfield code="0">(DE-588)4003972-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Hardy-Raum</subfield><subfield code="0">(DE-588)4159109-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/b95203</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027859002</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><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\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.BV042423585 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783764378042 9783764370596 |
| issn | 1660-8046 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859002 |
| oclc_num | 837759527 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XV, 168 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Birkhäuser Basel |
| record_format | marc |
| series2 | Frontiers in Mathematics |
| spelling | Krausshar, Rolf Sören Verfasser aut Generalized Analytic Automorphic Forms in Hypercomplex Spaces by Rolf Sören Krausshar Basel Birkhäuser Basel 2004 1 Online-Ressource (XV, 168 p) txt rdacontent c rdamedia cr rdacarrier Frontiers in Mathematics 1660-8046 This book describes the basic theory of hypercomplex-analytic automorphic forms and functions for arithmetic subgroups of the Vahlen group in higher dimensional spaces. Hypercomplex analyticity generalizes the concept of complex analyticity in the sense of considering null-solutions to higher dimensional Cauchy-Riemann type systems. Vector- and Clifford algebra-valued Eisenstein and Poincaré series are constructed within this framework and a detailed description of their analytic and number theoretical properties is provided. In particular, explicit relationships to generalized variants of the Riemann zeta function and Dirichlet L-series are established and a concept of hypercomplex multiplication of lattices is introduced. Applications to the theory of Hilbert spaces with reproducing kernels, to partial differential equations and index theory on some conformal manifolds are also described Mathematics Integral Transforms Potential theory (Mathematics) Sequences (Mathematics) Functions, special Number theory Special Functions Integral Transforms, Operational Calculus Potential Theory Sequences, Series, Summability Number Theory Mathematik Automorphe Form (DE-588)4003972-9 gnd rswk-swf Hardy-Raum (DE-588)4159109-4 gnd rswk-swf Automorphe Form (DE-588)4003972-9 s 1\p DE-604 Hardy-Raum (DE-588)4159109-4 s 2\p DE-604 https://doi.org/10.1007/b95203 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Krausshar, Rolf Sören Generalized Analytic Automorphic Forms in Hypercomplex Spaces Mathematics Integral Transforms Potential theory (Mathematics) Sequences (Mathematics) Functions, special Number theory Special Functions Integral Transforms, Operational Calculus Potential Theory Sequences, Series, Summability Number Theory Mathematik Automorphe Form (DE-588)4003972-9 gnd Hardy-Raum (DE-588)4159109-4 gnd |
| subject_GND | (DE-588)4003972-9 (DE-588)4159109-4 |
| title | Generalized Analytic Automorphic Forms in Hypercomplex Spaces |
| title_auth | Generalized Analytic Automorphic Forms in Hypercomplex Spaces |
| title_exact_search | Generalized Analytic Automorphic Forms in Hypercomplex Spaces |
| title_full | Generalized Analytic Automorphic Forms in Hypercomplex Spaces by Rolf Sören Krausshar |
| title_fullStr | Generalized Analytic Automorphic Forms in Hypercomplex Spaces by Rolf Sören Krausshar |
| title_full_unstemmed | Generalized Analytic Automorphic Forms in Hypercomplex Spaces by Rolf Sören Krausshar |
| title_short | Generalized Analytic Automorphic Forms in Hypercomplex Spaces |
| title_sort | generalized analytic automorphic forms in hypercomplex spaces |
| topic | Mathematics Integral Transforms Potential theory (Mathematics) Sequences (Mathematics) Functions, special Number theory Special Functions Integral Transforms, Operational Calculus Potential Theory Sequences, Series, Summability Number Theory Mathematik Automorphe Form (DE-588)4003972-9 gnd Hardy-Raum (DE-588)4159109-4 gnd |
| topic_facet | Mathematics Integral Transforms Potential theory (Mathematics) Sequences (Mathematics) Functions, special Number theory Special Functions Integral Transforms, Operational Calculus Potential Theory Sequences, Series, Summability Number Theory Mathematik Automorphe Form Hardy-Raum |
| url | https://doi.org/10.1007/b95203 |
| work_keys_str_mv | AT kraussharrolfsoren generalizedanalyticautomorphicformsinhypercomplexspaces |