The quaternionic Maass Spezialschar on split \(\mathrm{SO}(8)\)

The quaternionic Maass Spezialschar on split \(\mathrm{SO}(8)\)

The classical Maass Spezialschar is a Hecke-stable subspace of the level one holomorphic Siegel modular forms of genus two, i.e., on \(\mathrm{Sp}_4\), cut out by certain linear relations between the Fourier coefficients. It is a theorem of Andrianov, Maass, and Zagier, that the classical Maass Spez...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2024-01
Hauptverfasser: Johnson-Leung, Jennifer, McGlade, Finn, Negrini, Isabella, Pollack, Aaron, Roy, Manami
Format: Artikel
Sprache:eng
Schlagworte:
Analytic functions
Theorems
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Johnson-Leung, Jennifer
McGlade, Finn
Negrini, Isabella
Pollack, Aaron
Roy, Manami
description The classical Maass Spezialschar is a Hecke-stable subspace of the level one holomorphic Siegel modular forms of genus two, i.e., on \(\mathrm{Sp}_4\), cut out by certain linear relations between the Fourier coefficients. It is a theorem of Andrianov, Maass, and Zagier, that the classical Maass Spezialschar is exactly equal to the space of Saito-Kurokawa lifts. We study an analogous space of quaternionic modular forms on split \(\mathrm{SO}_8\), and prove the analogue of the Andrianov-Maass-Zagier theorem. Our main tool for proving this theorem is the development of a theory of a Fourier-Jacobi expansion of quaternionic modular forms on orthogonal groups.
format Article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2919925982</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2919925982</sourcerecordid><originalsourceid>FETCH-proquest_journals_29199259823</originalsourceid><addsrcrecordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mSwD8lIVSgsTSxJLcrLzM_LTFbwTUwsLlYILkitykzMKU7OSCxSyM9TKC7IySxRiNGIyU0sySjKrQ72r9Ww0IzR5GFgTQMqS-WF0twMym6uIc4eugVF-YWlqcUl8Vn5pUV5QKl4I0tDS0sjU0sLI2PiVAEAwTA4Hw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2919925982</pqid></control><display><type>article</type><title>The quaternionic Maass Spezialschar on split \(\mathrm{SO}(8)\)</title><source>Free E- Journals</source><creator>Johnson-Leung, Jennifer ; McGlade, Finn ; Negrini, Isabella ; Pollack, Aaron ; Roy, Manami</creator><creatorcontrib>Johnson-Leung, Jennifer ; McGlade, Finn ; Negrini, Isabella ; Pollack, Aaron ; Roy, Manami</creatorcontrib><description>The classical Maass Spezialschar is a Hecke-stable subspace of the level one holomorphic Siegel modular forms of genus two, i.e., on \(\mathrm{Sp}_4\), cut out by certain linear relations between the Fourier coefficients. It is a theorem of Andrianov, Maass, and Zagier, that the classical Maass Spezialschar is exactly equal to the space of Saito-Kurokawa lifts. We study an analogous space of quaternionic modular forms on split \(\mathrm{SO}_8\), and prove the analogue of the Andrianov-Maass-Zagier theorem. Our main tool for proving this theorem is the development of a theory of a Fourier-Jacobi expansion of quaternionic modular forms on orthogonal groups.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Analytic functions ; Theorems</subject><ispartof>arXiv.org, 2024-01</ispartof><rights>2024. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>776,780</link.rule.ids></links><search><creatorcontrib>Johnson-Leung, Jennifer</creatorcontrib><creatorcontrib>McGlade, Finn</creatorcontrib><creatorcontrib>Negrini, Isabella</creatorcontrib><creatorcontrib>Pollack, Aaron</creatorcontrib><creatorcontrib>Roy, Manami</creatorcontrib><title>The quaternionic Maass Spezialschar on split \(\mathrm{SO}(8)\)</title><title>arXiv.org</title><description>The classical Maass Spezialschar is a Hecke-stable subspace of the level one holomorphic Siegel modular forms of genus two, i.e., on \(\mathrm{Sp}_4\), cut out by certain linear relations between the Fourier coefficients. It is a theorem of Andrianov, Maass, and Zagier, that the classical Maass Spezialschar is exactly equal to the space of Saito-Kurokawa lifts. We study an analogous space of quaternionic modular forms on split \(\mathrm{SO}_8\), and prove the analogue of the Andrianov-Maass-Zagier theorem. Our main tool for proving this theorem is the development of a theory of a Fourier-Jacobi expansion of quaternionic modular forms on orthogonal groups.</description><subject>Analytic functions</subject><subject>Theorems</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mSwD8lIVSgsTSxJLcrLzM_LTFbwTUwsLlYILkitykzMKU7OSCxSyM9TKC7IySxRiNGIyU0sySjKrQ72r9Ww0IzR5GFgTQMqS-WF0twMym6uIc4eugVF-YWlqcUl8Vn5pUV5QKl4I0tDS0sjU0sLI2PiVAEAwTA4Hw</recordid><startdate>20240127</startdate><enddate>20240127</enddate><creator>Johnson-Leung, Jennifer</creator><creator>McGlade, Finn</creator><creator>Negrini, Isabella</creator><creator>Pollack, Aaron</creator><creator>Roy, Manami</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20240127</creationdate><title>The quaternionic Maass Spezialschar on split \(\mathrm{SO}(8)\)</title><author>Johnson-Leung, Jennifer ; McGlade, Finn ; Negrini, Isabella ; Pollack, Aaron ; Roy, Manami</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_29199259823</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Analytic functions</topic><topic>Theorems</topic><toplevel>online_resources</toplevel><creatorcontrib>Johnson-Leung, Jennifer</creatorcontrib><creatorcontrib>McGlade, Finn</creatorcontrib><creatorcontrib>Negrini, Isabella</creatorcontrib><creatorcontrib>Pollack, Aaron</creatorcontrib><creatorcontrib>Roy, Manami</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Johnson-Leung, Jennifer</au><au>McGlade, Finn</au><au>Negrini, Isabella</au><au>Pollack, Aaron</au><au>Roy, Manami</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>The quaternionic Maass Spezialschar on split \(\mathrm{SO}(8)\)</atitle><jtitle>arXiv.org</jtitle><date>2024-01-27</date><risdate>2024</risdate><eissn>2331-8422</eissn><abstract>The classical Maass Spezialschar is a Hecke-stable subspace of the level one holomorphic Siegel modular forms of genus two, i.e., on \(\mathrm{Sp}_4\), cut out by certain linear relations between the Fourier coefficients. It is a theorem of Andrianov, Maass, and Zagier, that the classical Maass Spezialschar is exactly equal to the space of Saito-Kurokawa lifts. We study an analogous space of quaternionic modular forms on split \(\mathrm{SO}_8\), and prove the analogue of the Andrianov-Maass-Zagier theorem. Our main tool for proving this theorem is the development of a theory of a Fourier-Jacobi expansion of quaternionic modular forms on orthogonal groups.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2024-01
issn 2331-8422
language eng
recordid cdi_proquest_journals_2919925982
source Free E- Journals
subjects Analytic functions
Theorems
title The quaternionic Maass Spezialschar on split \(\mathrm{SO}(8)\)
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-23T23%3A44%3A19IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=The%20quaternionic%20Maass%20Spezialschar%20on%20split%20%5C(%5Cmathrm%7BSO%7D(8)%5C)&rft.jtitle=arXiv.org&rft.au=Johnson-Leung,%20Jennifer&rft.date=2024-01-27&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2919925982%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2919925982&rft_id=info:pmid/&rfr_iscdi=true