The Arithmetic and Spectral Analysis of Poincaré Series:
The Arithmetic and Spectral Analysis of Poincaré series deals with the spectral properties of Poincaré series and their relation to Kloosterman sums. In addition to Poincaré series for an arbitrary Fuchsian group of the first kind, the spectral expansion of the Kloosterman-Selberg zeta function is a...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Kent
Elsevier Science
2014
|
| Schriftenreihe: | Perspectives in Mathematics
v.13 |
| Schlagworte: | |
| Online-Zugang: | DE-1046 |
| Zusammenfassung: | The Arithmetic and Spectral Analysis of Poincaré series deals with the spectral properties of Poincaré series and their relation to Kloosterman sums. In addition to Poincaré series for an arbitrary Fuchsian group of the first kind, the spectral expansion of the Kloosterman-Selberg zeta function is analyzed, along with the adellic theory of Poincaré series and Kloosterman sums over a global function field. This volume is divided into two parts and begins with a discussion on Poincaré series and Kloosterman sums for Fuchsian groups of the first kind. A conceptual proof of Kuznetsov's formula and its generalization are presented in terms of the spectral analysis of Poincaré series in the framework of representation theory. An analysis of the spectral expansion of the Kloosterman-Selberg zeta function is also included. The second part develops the adellic theory of Poincaré series and Kloosterman sums over a global function field. The main result here is to show that in this context the analogue of the Linnik conjecture can be derived from the Ramanujan conjecture over function fields. Whittaker models, Kirillov models, and Bessel functions are also considered, along with the Kloosterman-spectral formula, convergence, and continuation.This book will be a valuable resource for students of mathematics |
| Beschreibung: | Description based on publisher supplied metadata and other sources |
| Beschreibung: | 1 online resource (190 pages) |
| ISBN: | 9781483266176 9780121785901 |
Internformat
MARC
| LEADER | 00000nam a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV043616716 | ||
| 003 | DE-604 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 160616s2014 xx o|||| 00||| eng d | ||
| 020 | |a 9781483266176 |9 978-1-4832-6617-6 | ||
| 020 | |a 9780121785901 |c Print |9 978-0-12-178590-1 | ||
| 035 | |a (ZDB-30-PQE)EBC1901543 | ||
| 035 | |a (ZDB-89-EBL)EBL1901543 | ||
| 035 | |a (ZDB-38-EBR)ebr11008560 | ||
| 035 | |a (OCoLC)679979363 | ||
| 035 | |a (DE-599)BVBBV043616716 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-1046 | ||
| 082 | 0 | |a 519.5 | |
| 100 | 1 | |a Cogdell, James W. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The Arithmetic and Spectral Analysis of Poincaré Series |
| 264 | 1 | |a Kent |b Elsevier Science |c 2014 | |
| 264 | 4 | |c © 1990 | |
| 300 | |a 1 online resource (190 pages) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Perspectives in Mathematics |v v.13 | |
| 500 | |a Description based on publisher supplied metadata and other sources | ||
| 520 | |a The Arithmetic and Spectral Analysis of Poincaré series deals with the spectral properties of Poincaré series and their relation to Kloosterman sums. In addition to Poincaré series for an arbitrary Fuchsian group of the first kind, the spectral expansion of the Kloosterman-Selberg zeta function is analyzed, along with the adellic theory of Poincaré series and Kloosterman sums over a global function field. This volume is divided into two parts and begins with a discussion on Poincaré series and Kloosterman sums for Fuchsian groups of the first kind. A conceptual proof of Kuznetsov's formula and its generalization are presented in terms of the spectral analysis of Poincaré series in the framework of representation theory. An analysis of the spectral expansion of the Kloosterman-Selberg zeta function is also included. The second part develops the adellic theory of Poincaré series and Kloosterman sums over a global function field. The main result here is to show that in this context the analogue of the Linnik conjecture can be derived from the Ramanujan conjecture over function fields. Whittaker models, Kirillov models, and Bessel functions are also considered, along with the Kloosterman-spectral formula, convergence, and continuation.This book will be a valuable resource for students of mathematics | ||
| 650 | 4 | |a Poincaré series | |
| 650 | 4 | |a Spectral theory (Mathematics) | |
| 650 | 0 | 7 | |a Poincaré-Reihe |0 (DE-588)4174967-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Spektraltheorie |0 (DE-588)4116561-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Zetafunktion |0 (DE-588)4190764-4 |2 gnd |9 rswk-swf |
| 655 | 7 | |8 1\p |0 (DE-588)4143413-4 |a Aufsatzsammlung |2 gnd-content | |
| 689 | 0 | 0 | |a Poincaré-Reihe |0 (DE-588)4174967-4 |D s |
| 689 | 0 | 1 | |a Spektraltheorie |0 (DE-588)4116561-5 |D s |
| 689 | 0 | |8 2\p |5 DE-604 | |
| 689 | 1 | 0 | |a Zetafunktion |0 (DE-588)4190764-4 |D s |
| 689 | 1 | |8 3\p |5 DE-604 | |
| 700 | 1 | |a Piatetski-Shapiro, Iiya |e Sonstige |4 oth | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |a Cogdell, James W |t . The Arithmetic and Spectral Analysis of Poincaré Series |
| 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 | |
| 883 | 1 | |8 3\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 912 | |a ZDB-30-PQE | ||
| 912 | |a ZDB-33-ESD | ||
| 912 | |a ZDB-33-EBS | ||
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-029030775 | |
| 966 | e | |u http://www.sciencedirect.com/science/book/9780121785901 |l DE-1046 |p ZDB-33-ESD |q FAW_PDA_ESD |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1825578095667576832 |
|---|---|
| adam_text | |
| any_adam_object | |
| author | Cogdell, James W. |
| author_facet | Cogdell, James W. |
| author_role | aut |
| author_sort | Cogdell, James W. |
| author_variant | j w c jw jwc |
| building | Verbundindex |
| bvnumber | BV043616716 |
| collection | ZDB-30-PQE ZDB-33-ESD ZDB-33-EBS |
| ctrlnum | (ZDB-30-PQE)EBC1901543 (ZDB-89-EBL)EBL1901543 (ZDB-38-EBR)ebr11008560 (OCoLC)679979363 (DE-599)BVBBV043616716 |
| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000zcb4500</leader><controlfield tag="001">BV043616716</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">160616s2014 xx o|||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781483266176</subfield><subfield code="9">978-1-4832-6617-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780121785901</subfield><subfield code="c">Print</subfield><subfield code="9">978-0-12-178590-1</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-30-PQE)EBC1901543</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-89-EBL)EBL1901543</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-38-EBR)ebr11008560</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)679979363</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043616716</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-1046</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.5</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Cogdell, James W.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The Arithmetic and Spectral Analysis of Poincaré Series</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Kent</subfield><subfield code="b">Elsevier Science</subfield><subfield code="c">2014</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 1990</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (190 pages)</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">Perspectives in Mathematics</subfield><subfield code="v">v.13</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Description based on publisher supplied metadata and other sources</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The Arithmetic and Spectral Analysis of Poincaré series deals with the spectral properties of Poincaré series and their relation to Kloosterman sums. In addition to Poincaré series for an arbitrary Fuchsian group of the first kind, the spectral expansion of the Kloosterman-Selberg zeta function is analyzed, along with the adellic theory of Poincaré series and Kloosterman sums over a global function field. This volume is divided into two parts and begins with a discussion on Poincaré series and Kloosterman sums for Fuchsian groups of the first kind. A conceptual proof of Kuznetsov's formula and its generalization are presented in terms of the spectral analysis of Poincaré series in the framework of representation theory. An analysis of the spectral expansion of the Kloosterman-Selberg zeta function is also included. The second part develops the adellic theory of Poincaré series and Kloosterman sums over a global function field. The main result here is to show that in this context the analogue of the Linnik conjecture can be derived from the Ramanujan conjecture over function fields. Whittaker models, Kirillov models, and Bessel functions are also considered, along with the Kloosterman-spectral formula, convergence, and continuation.This book will be a valuable resource for students of mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Poincaré series</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Spectral theory (Mathematics)</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Poincaré-Reihe</subfield><subfield code="0">(DE-588)4174967-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Spektraltheorie</subfield><subfield code="0">(DE-588)4116561-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Zetafunktion</subfield><subfield code="0">(DE-588)4190764-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="8">1\p</subfield><subfield code="0">(DE-588)4143413-4</subfield><subfield code="a">Aufsatzsammlung</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Poincaré-Reihe</subfield><subfield code="0">(DE-588)4174967-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Spektraltheorie</subfield><subfield code="0">(DE-588)4116561-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Zetafunktion</subfield><subfield code="0">(DE-588)4190764-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">3\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Piatetski-Shapiro, Iiya</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="a">Cogdell, James W</subfield><subfield code="t">. The Arithmetic and Spectral Analysis of Poincaré Series</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><datafield tag="883" ind1="1" ind2=" "><subfield code="8">3\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="912" ind1=" " ind2=" "><subfield code="a">ZDB-30-PQE</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-33-ESD</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-33-EBS</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-029030775</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">http://www.sciencedirect.com/science/book/9780121785901</subfield><subfield code="l">DE-1046</subfield><subfield code="p">ZDB-33-ESD</subfield><subfield code="q">FAW_PDA_ESD</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| genre | 1\p (DE-588)4143413-4 Aufsatzsammlung gnd-content |
| genre_facet | Aufsatzsammlung |
| id | DE-604.BV043616716 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-03T13:02:22Z |
| institution | BVB |
| isbn | 9781483266176 9780121785901 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029030775 |
| oclc_num | 679979363 |
| open_access_boolean | |
| owner | DE-1046 |
| owner_facet | DE-1046 |
| physical | 1 online resource (190 pages) |
| psigel | ZDB-30-PQE ZDB-33-ESD ZDB-33-EBS ZDB-33-ESD FAW_PDA_ESD |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Elsevier Science |
| record_format | marc |
| series2 | Perspectives in Mathematics |
| spelling | Cogdell, James W. Verfasser aut The Arithmetic and Spectral Analysis of Poincaré Series Kent Elsevier Science 2014 © 1990 1 online resource (190 pages) txt rdacontent c rdamedia cr rdacarrier Perspectives in Mathematics v.13 Description based on publisher supplied metadata and other sources The Arithmetic and Spectral Analysis of Poincaré series deals with the spectral properties of Poincaré series and their relation to Kloosterman sums. In addition to Poincaré series for an arbitrary Fuchsian group of the first kind, the spectral expansion of the Kloosterman-Selberg zeta function is analyzed, along with the adellic theory of Poincaré series and Kloosterman sums over a global function field. This volume is divided into two parts and begins with a discussion on Poincaré series and Kloosterman sums for Fuchsian groups of the first kind. A conceptual proof of Kuznetsov's formula and its generalization are presented in terms of the spectral analysis of Poincaré series in the framework of representation theory. An analysis of the spectral expansion of the Kloosterman-Selberg zeta function is also included. The second part develops the adellic theory of Poincaré series and Kloosterman sums over a global function field. The main result here is to show that in this context the analogue of the Linnik conjecture can be derived from the Ramanujan conjecture over function fields. Whittaker models, Kirillov models, and Bessel functions are also considered, along with the Kloosterman-spectral formula, convergence, and continuation.This book will be a valuable resource for students of mathematics Poincaré series Spectral theory (Mathematics) Poincaré-Reihe (DE-588)4174967-4 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Zetafunktion (DE-588)4190764-4 gnd rswk-swf 1\p (DE-588)4143413-4 Aufsatzsammlung gnd-content Poincaré-Reihe (DE-588)4174967-4 s Spektraltheorie (DE-588)4116561-5 s 2\p DE-604 Zetafunktion (DE-588)4190764-4 s 3\p DE-604 Piatetski-Shapiro, Iiya Sonstige oth Erscheint auch als Druck-Ausgabe Cogdell, James W . The Arithmetic and Spectral Analysis of Poincaré Series 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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cogdell, James W. The Arithmetic and Spectral Analysis of Poincaré Series Poincaré series Spectral theory (Mathematics) Poincaré-Reihe (DE-588)4174967-4 gnd Spektraltheorie (DE-588)4116561-5 gnd Zetafunktion (DE-588)4190764-4 gnd |
| subject_GND | (DE-588)4174967-4 (DE-588)4116561-5 (DE-588)4190764-4 (DE-588)4143413-4 |
| title | The Arithmetic and Spectral Analysis of Poincaré Series |
| title_auth | The Arithmetic and Spectral Analysis of Poincaré Series |
| title_exact_search | The Arithmetic and Spectral Analysis of Poincaré Series |
| title_full | The Arithmetic and Spectral Analysis of Poincaré Series |
| title_fullStr | The Arithmetic and Spectral Analysis of Poincaré Series |
| title_full_unstemmed | The Arithmetic and Spectral Analysis of Poincaré Series |
| title_short | The Arithmetic and Spectral Analysis of Poincaré Series |
| title_sort | the arithmetic and spectral analysis of poincare series |
| topic | Poincaré series Spectral theory (Mathematics) Poincaré-Reihe (DE-588)4174967-4 gnd Spektraltheorie (DE-588)4116561-5 gnd Zetafunktion (DE-588)4190764-4 gnd |
| topic_facet | Poincaré series Spectral theory (Mathematics) Poincaré-Reihe Spektraltheorie Zetafunktion Aufsatzsammlung |
| work_keys_str_mv | AT cogdelljamesw thearithmeticandspectralanalysisofpoincareseries AT piatetskishapiroiiya thearithmeticandspectralanalysisofpoincareseries |