Zeros of dirichlet L‐functions near the critical line
We prove an upper bound on the density of zeros very close to the critical line of the family of Dirichlet L‐functions of modulus q at height T. To do this, we derive an asymptotic for the twisted second moment of Dirichlet L‐functions uniformly in q and t. As a second application of the asymptotic...
Gespeichert in:
| Veröffentlicht in: | Mathematika 2024-01, Vol.70 (1), p.n/a |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | n/a |
|---|---|
| container_issue | 1 |
| container_start_page | |
| container_title | Mathematika |
| container_volume | 70 |
| creator | Dickinson, George |
| description | We prove an upper bound on the density of zeros very close to the critical line of the family of Dirichlet L‐functions of modulus q at height T. To do this, we derive an asymptotic for the twisted second moment of Dirichlet L‐functions uniformly in q and t. As a second application of the asymptotic formula, we prove that, for every integer q, at least 38.2% of zeros of the primitive Dirichlet L‐functions of modulus q lie on the critical line. |
| doi_str_mv | 10.1112/mtk.12239 |
| format | Article |
| fullrecord | <record><control><sourceid>wiley_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1112_mtk_12239</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>MTK12239</sourcerecordid><originalsourceid>FETCH-LOGICAL-c2649-3efb8741044f9adce000447052848bfa07d361d0a58e1c58442c00508d5272d3</originalsourceid><addsrcrecordid>eNp1jztOxDAURS0EEmGgYAduKTLz7NixU6IRPxFEk4rG8vijMWQSZBuh6VgCa2QlBEJLdW9x3tM9CJ0TWBJC6GqXX5aE0qo5QAUFRkrRMHqICgDKSy6a6hidpPQMwGvJSIHEk4tjwqPHNsRgtr3LuP36-PRvg8lhHBIenI44bx02MeRgdI_7MLhTdOR1n9zZXy5Qd33VrW_L9vHmbn3ZlobWrCkr5zdSMAKM-UZb4wCmKoBTyeTGaxC2qokFzaUjhkvGqJm2gbScCmqrBbqY35ppZYrOq9cYdjruFQH1I6wmYfUrPLGrmX0Pvdv_D6qH7n6--AYcV1b1</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Zeros of dirichlet L‐functions near the critical line</title><source>Wiley Online Library All Journals</source><creator>Dickinson, George</creator><creatorcontrib>Dickinson, George</creatorcontrib><description>We prove an upper bound on the density of zeros very close to the critical line of the family of Dirichlet L‐functions of modulus q at height T. To do this, we derive an asymptotic for the twisted second moment of Dirichlet L‐functions uniformly in q and t. As a second application of the asymptotic formula, we prove that, for every integer q, at least 38.2% of zeros of the primitive Dirichlet L‐functions of modulus q lie on the critical line.</description><identifier>ISSN: 0025-5793</identifier><identifier>EISSN: 2041-7942</identifier><identifier>DOI: 10.1112/mtk.12239</identifier><language>eng</language><ispartof>Mathematika, 2024-01, Vol.70 (1), p.n/a</ispartof><rights>2024 The Authors. is copyright © University College London and published by the London Mathematical Society on behalf of University College London.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c2649-3efb8741044f9adce000447052848bfa07d361d0a58e1c58442c00508d5272d3</cites><orcidid>0000-0002-4248-9858</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1112%2Fmtk.12239$$EPDF$$P50$$Gwiley$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1112%2Fmtk.12239$$EHTML$$P50$$Gwiley$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,1411,27903,27904,45553,45554</link.rule.ids></links><search><creatorcontrib>Dickinson, George</creatorcontrib><title>Zeros of dirichlet L‐functions near the critical line</title><title>Mathematika</title><description>We prove an upper bound on the density of zeros very close to the critical line of the family of Dirichlet L‐functions of modulus q at height T. To do this, we derive an asymptotic for the twisted second moment of Dirichlet L‐functions uniformly in q and t. As a second application of the asymptotic formula, we prove that, for every integer q, at least 38.2% of zeros of the primitive Dirichlet L‐functions of modulus q lie on the critical line.</description><issn>0025-5793</issn><issn>2041-7942</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>24P</sourceid><recordid>eNp1jztOxDAURS0EEmGgYAduKTLz7NixU6IRPxFEk4rG8vijMWQSZBuh6VgCa2QlBEJLdW9x3tM9CJ0TWBJC6GqXX5aE0qo5QAUFRkrRMHqICgDKSy6a6hidpPQMwGvJSIHEk4tjwqPHNsRgtr3LuP36-PRvg8lhHBIenI44bx02MeRgdI_7MLhTdOR1n9zZXy5Qd33VrW_L9vHmbn3ZlobWrCkr5zdSMAKM-UZb4wCmKoBTyeTGaxC2qokFzaUjhkvGqJm2gbScCmqrBbqY35ppZYrOq9cYdjruFQH1I6wmYfUrPLGrmX0Pvdv_D6qH7n6--AYcV1b1</recordid><startdate>202401</startdate><enddate>202401</enddate><creator>Dickinson, George</creator><scope>24P</scope><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-4248-9858</orcidid></search><sort><creationdate>202401</creationdate><title>Zeros of dirichlet L‐functions near the critical line</title><author>Dickinson, George</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2649-3efb8741044f9adce000447052848bfa07d361d0a58e1c58442c00508d5272d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dickinson, George</creatorcontrib><collection>Wiley-Blackwell Open Access Titles</collection><collection>CrossRef</collection><jtitle>Mathematika</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dickinson, George</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Zeros of dirichlet L‐functions near the critical line</atitle><jtitle>Mathematika</jtitle><date>2024-01</date><risdate>2024</risdate><volume>70</volume><issue>1</issue><epage>n/a</epage><issn>0025-5793</issn><eissn>2041-7942</eissn><abstract>We prove an upper bound on the density of zeros very close to the critical line of the family of Dirichlet L‐functions of modulus q at height T. To do this, we derive an asymptotic for the twisted second moment of Dirichlet L‐functions uniformly in q and t. As a second application of the asymptotic formula, we prove that, for every integer q, at least 38.2% of zeros of the primitive Dirichlet L‐functions of modulus q lie on the critical line.</abstract><doi>10.1112/mtk.12239</doi><tpages>35</tpages><orcidid>https://orcid.org/0000-0002-4248-9858</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0025-5793 |
| ispartof | Mathematika, 2024-01, Vol.70 (1), p.n/a |
| issn | 0025-5793 2041-7942 |
| language | eng |
| recordid | cdi_crossref_primary_10_1112_mtk_12239 |
| source | Wiley Online Library All Journals |
| title | Zeros of dirichlet L‐functions near the critical line |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-25T16%3A06%3A05IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-wiley_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Zeros%20of%20dirichlet%20L%E2%80%90functions%20near%20the%20critical%20line&rft.jtitle=Mathematika&rft.au=Dickinson,%20George&rft.date=2024-01&rft.volume=70&rft.issue=1&rft.epage=n/a&rft.issn=0025-5793&rft.eissn=2041-7942&rft_id=info:doi/10.1112/mtk.12239&rft_dat=%3Cwiley_cross%3EMTK12239%3C/wiley_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |