Quantum Limits of Eisenstein Series in H^3

We study the quantum limits of Eisenstein series off the critical line for \(\mathrm{PSL}_{2}(\mathcal{O}_{K})\backslash\mathbb{H}^{3}\), where \(K\) is an imaginary quadratic field of class number one. This generalises the results of Petridis, Raulf and Risager on \(\mathrm{PSL}_{2}(\mathbb{Z})\bac...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2015-11
Main Author: Laaksonen, Niko
Format: Article
Language:English
Subjects:
Fields (mathematics)
Number theory
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Laaksonen, Niko
description We study the quantum limits of Eisenstein series off the critical line for \(\mathrm{PSL}_{2}(\mathcal{O}_{K})\backslash\mathbb{H}^{3}\), where \(K\) is an imaginary quadratic field of class number one. This generalises the results of Petridis, Raulf and Risager on \(\mathrm{PSL}_{2}(\mathbb{Z})\backslash\mathbb{H}^{2}\). We observe that the measures \(\lvert E(p,\sigma_{t}+it)\rvert^{2}d\mu(p)\) become equidistributed only if \(\sigma_{t}\rightarrow 1\) as \(t\rightarrow\infty\). We use these computations to study measures defined in terms of the scattering states, which are shown to converge to the absolutely continuous measure \(E(p,3)d\mu(p)\) under the GRH.
format article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2083862452</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2083862452</sourcerecordid><originalsourceid>FETCH-proquest_journals_20838624523</originalsourceid><addsrcrecordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mTQCixNzCspzVXwyczNLClWyE9TcM0sTs0rLknNzFMITi3KTC1WALI84ox5GFjTEnOKU3mhNDeDsptriLOHbkFRfmFpanFJfFZ-aVEeUCreyMDC2MLMyMTUyJg4VQDQhTAj</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2083862452</pqid></control><display><type>article</type><title>Quantum Limits of Eisenstein Series in H^3</title><source>Publicly Available Content Database</source><creator>Laaksonen, Niko</creator><creatorcontrib>Laaksonen, Niko</creatorcontrib><description>We study the quantum limits of Eisenstein series off the critical line for \(\mathrm{PSL}_{2}(\mathcal{O}_{K})\backslash\mathbb{H}^{3}\), where \(K\) is an imaginary quadratic field of class number one. This generalises the results of Petridis, Raulf and Risager on \(\mathrm{PSL}_{2}(\mathbb{Z})\backslash\mathbb{H}^{2}\). We observe that the measures \(\lvert E(p,\sigma_{t}+it)\rvert^{2}d\mu(p)\) become equidistributed only if \(\sigma_{t}\rightarrow 1\) as \(t\rightarrow\infty\). We use these computations to study measures defined in terms of the scattering states, which are shown to converge to the absolutely continuous measure \(E(p,3)d\mu(p)\) under the GRH.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Fields (mathematics) ; Number theory</subject><ispartof>arXiv.org, 2015-11</ispartof><rights>2015. 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>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/2083862452?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>776,780,25731,36989,44566</link.rule.ids></links><search><creatorcontrib>Laaksonen, Niko</creatorcontrib><title>Quantum Limits of Eisenstein Series in H^3</title><title>arXiv.org</title><description>We study the quantum limits of Eisenstein series off the critical line for \(\mathrm{PSL}_{2}(\mathcal{O}_{K})\backslash\mathbb{H}^{3}\), where \(K\) is an imaginary quadratic field of class number one. This generalises the results of Petridis, Raulf and Risager on \(\mathrm{PSL}_{2}(\mathbb{Z})\backslash\mathbb{H}^{2}\). We observe that the measures \(\lvert E(p,\sigma_{t}+it)\rvert^{2}d\mu(p)\) become equidistributed only if \(\sigma_{t}\rightarrow 1\) as \(t\rightarrow\infty\). We use these computations to study measures defined in terms of the scattering states, which are shown to converge to the absolutely continuous measure \(E(p,3)d\mu(p)\) under the GRH.</description><subject>Fields (mathematics)</subject><subject>Number theory</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><recordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mTQCixNzCspzVXwyczNLClWyE9TcM0sTs0rLknNzFMITi3KTC1WALI84ox5GFjTEnOKU3mhNDeDsptriLOHbkFRfmFpanFJfFZ-aVEeUCreyMDC2MLMyMTUyJg4VQDQhTAj</recordid><startdate>20151123</startdate><enddate>20151123</enddate><creator>Laaksonen, Niko</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>20151123</creationdate><title>Quantum Limits of Eisenstein Series in H^3</title><author>Laaksonen, Niko</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_20838624523</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Fields (mathematics)</topic><topic>Number theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Laaksonen, Niko</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</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>Laaksonen, Niko</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Quantum Limits of Eisenstein Series in H^3</atitle><jtitle>arXiv.org</jtitle><date>2015-11-23</date><risdate>2015</risdate><eissn>2331-8422</eissn><abstract>We study the quantum limits of Eisenstein series off the critical line for \(\mathrm{PSL}_{2}(\mathcal{O}_{K})\backslash\mathbb{H}^{3}\), where \(K\) is an imaginary quadratic field of class number one. This generalises the results of Petridis, Raulf and Risager on \(\mathrm{PSL}_{2}(\mathbb{Z})\backslash\mathbb{H}^{2}\). We observe that the measures \(\lvert E(p,\sigma_{t}+it)\rvert^{2}d\mu(p)\) become equidistributed only if \(\sigma_{t}\rightarrow 1\) as \(t\rightarrow\infty\). We use these computations to study measures defined in terms of the scattering states, which are shown to converge to the absolutely continuous measure \(E(p,3)d\mu(p)\) under the GRH.</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, 2015-11
issn 2331-8422
language eng
recordid cdi_proquest_journals_2083862452
source Publicly Available Content Database
subjects Fields (mathematics)
Number theory
title Quantum Limits of Eisenstein Series in H^3
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-02T20%3A25%3A39IST&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=Quantum%20Limits%20of%20Eisenstein%20Series%20in%20H%5E3&rft.jtitle=arXiv.org&rft.au=Laaksonen,%20Niko&rft.date=2015-11-23&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2083862452%3C/proquest%3E%3Cgrp_id%3Ecdi_FETCH-proquest_journals_20838624523%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2083862452&rft_id=info:pmid/&rfr_iscdi=true