The Size of the Lerch Zeta-Function at Places Symmetric with Respect to the Line ℜ(s) = 1/2

Let ζ( s ) be the Riemann zeta-function. If t ⩾ 6.8 and σ > 1/2, then it is known that the inequality |ζ(1 − s )| > |ζ( s )| is valid except at the zeros of ζ( s ). Here we investigate the Lerch zeta-function L ( λ , α , s ) which usually has many zeros off the critical line and it is expected...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Czechoslovak mathematical journal 2019-03, Vol.69 (1), p.25-37
Hauptverfasser: Garunkštis, Ramūnas, Grigutis, Andrius
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 37
container_issue 1
container_start_page 25
container_title Czechoslovak mathematical journal
container_volume 69
creator Garunkštis, Ramūnas
Grigutis, Andrius
description Let ζ( s ) be the Riemann zeta-function. If t ⩾ 6.8 and σ > 1/2, then it is known that the inequality |ζ(1 − s )| > |ζ( s )| is valid except at the zeros of ζ( s ). Here we investigate the Lerch zeta-function L ( λ , α , s ) which usually has many zeros off the critical line and it is expected that these zeros are asymmetrically distributed with respect to the critical line. However, for equal parameters λ = α it is still possible to obtain a certain version of the inequality | L ( λ , λ , 1 − s ¯ )| > | L ( λ , λ , s)|.
doi_str_mv 10.21136/CMJ.2018.0149-17
format Article
fullrecord <record><control><sourceid>proquest_sprin</sourceid><recordid>TN_cdi_proquest_journals_2191385609</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2191385609</sourcerecordid><originalsourceid>FETCH-LOGICAL-p226t-13c7b608efe6c1657c58d10acf7538149f8b4ba252f9879afb9b27b4dbc9b8d13</originalsourceid><addsrcrecordid>eNpFkMtKAzEUhoMoWKsP4C7gRhfT5mQyuSxcSLFeqCi2bgQZkjSxU9qZ6SRFdO1j-HQ-iVMruDr_4jvn53wIHQPpUYCU9wd3tz1KQPYIMJWA2EEdyARNFDDYRR1CABLGGd1HByHMCSEpMNlBL5OZw-Piw-HK49jmkWvsDD-7qJPhurSxqEqsI35YaOsCHr8vly42hcVvRZzhRxdqZyOO1Xa3KB3-_vw6DWf4HEOfHqI9rxfBHf3NLnoaXk4G18no_upmcDFKakp5TCC1wnAinXfcAs-EzeQUiLZeZKls__HSMKNpRr2SQmlvlKHCsKmxyrRk2kUn27t1U63WLsR8Xq2bsq3MKShIZcaJaim6pULdFOWra_4pIPmvxrzVmG805huNOYj0B5WBZBo</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2191385609</pqid></control><display><type>article</type><title>The Size of the Lerch Zeta-Function at Places Symmetric with Respect to the Line ℜ(s) = 1/2</title><source>Springer Nature - Complete Springer Journals</source><source>Alma/SFX Local Collection</source><source>EZB Electronic Journals Library</source><creator>Garunkštis, Ramūnas ; Grigutis, Andrius</creator><creatorcontrib>Garunkštis, Ramūnas ; Grigutis, Andrius</creatorcontrib><description>Let ζ( s ) be the Riemann zeta-function. If t ⩾ 6.8 and σ &gt; 1/2, then it is known that the inequality |ζ(1 − s )| &gt; |ζ( s )| is valid except at the zeros of ζ( s ). Here we investigate the Lerch zeta-function L ( λ , α , s ) which usually has many zeros off the critical line and it is expected that these zeros are asymmetrically distributed with respect to the critical line. However, for equal parameters λ = α it is still possible to obtain a certain version of the inequality | L ( λ , λ , 1 − s ¯ )| &gt; | L ( λ , λ , s)|.</description><identifier>ISSN: 0011-4642</identifier><identifier>EISSN: 1572-9141</identifier><identifier>DOI: 10.21136/CMJ.2018.0149-17</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Analysis ; Convex and Discrete Geometry ; Mathematical Modeling and Industrial Mathematics ; Mathematics ; Mathematics and Statistics ; Ordinary Differential Equations</subject><ispartof>Czechoslovak mathematical journal, 2019-03, Vol.69 (1), p.25-37</ispartof><rights>Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2018</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-p226t-13c7b608efe6c1657c58d10acf7538149f8b4ba252f9879afb9b27b4dbc9b8d13</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.21136/CMJ.2018.0149-17$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.21136/CMJ.2018.0149-17$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51298</link.rule.ids></links><search><creatorcontrib>Garunkštis, Ramūnas</creatorcontrib><creatorcontrib>Grigutis, Andrius</creatorcontrib><title>The Size of the Lerch Zeta-Function at Places Symmetric with Respect to the Line ℜ(s) = 1/2</title><title>Czechoslovak mathematical journal</title><addtitle>Czech Math J</addtitle><description>Let ζ( s ) be the Riemann zeta-function. If t ⩾ 6.8 and σ &gt; 1/2, then it is known that the inequality |ζ(1 − s )| &gt; |ζ( s )| is valid except at the zeros of ζ( s ). Here we investigate the Lerch zeta-function L ( λ , α , s ) which usually has many zeros off the critical line and it is expected that these zeros are asymmetrically distributed with respect to the critical line. However, for equal parameters λ = α it is still possible to obtain a certain version of the inequality | L ( λ , λ , 1 − s ¯ )| &gt; | L ( λ , λ , s)|.</description><subject>Analysis</subject><subject>Convex and Discrete Geometry</subject><subject>Mathematical Modeling and Industrial Mathematics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Ordinary Differential Equations</subject><issn>0011-4642</issn><issn>1572-9141</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNpFkMtKAzEUhoMoWKsP4C7gRhfT5mQyuSxcSLFeqCi2bgQZkjSxU9qZ6SRFdO1j-HQ-iVMruDr_4jvn53wIHQPpUYCU9wd3tz1KQPYIMJWA2EEdyARNFDDYRR1CABLGGd1HByHMCSEpMNlBL5OZw-Piw-HK49jmkWvsDD-7qJPhurSxqEqsI35YaOsCHr8vly42hcVvRZzhRxdqZyOO1Xa3KB3-_vw6DWf4HEOfHqI9rxfBHf3NLnoaXk4G18no_upmcDFKakp5TCC1wnAinXfcAs-EzeQUiLZeZKls__HSMKNpRr2SQmlvlKHCsKmxyrRk2kUn27t1U63WLsR8Xq2bsq3MKShIZcaJaim6pULdFOWra_4pIPmvxrzVmG805huNOYj0B5WBZBo</recordid><startdate>20190301</startdate><enddate>20190301</enddate><creator>Garunkštis, Ramūnas</creator><creator>Grigutis, Andrius</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope/></search><sort><creationdate>20190301</creationdate><title>The Size of the Lerch Zeta-Function at Places Symmetric with Respect to the Line ℜ(s) = 1/2</title><author>Garunkštis, Ramūnas ; Grigutis, Andrius</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p226t-13c7b608efe6c1657c58d10acf7538149f8b4ba252f9879afb9b27b4dbc9b8d13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Analysis</topic><topic>Convex and Discrete Geometry</topic><topic>Mathematical Modeling and Industrial Mathematics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Ordinary Differential Equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Garunkštis, Ramūnas</creatorcontrib><creatorcontrib>Grigutis, Andrius</creatorcontrib><jtitle>Czechoslovak mathematical journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Garunkštis, Ramūnas</au><au>Grigutis, Andrius</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Size of the Lerch Zeta-Function at Places Symmetric with Respect to the Line ℜ(s) = 1/2</atitle><jtitle>Czechoslovak mathematical journal</jtitle><stitle>Czech Math J</stitle><date>2019-03-01</date><risdate>2019</risdate><volume>69</volume><issue>1</issue><spage>25</spage><epage>37</epage><pages>25-37</pages><issn>0011-4642</issn><eissn>1572-9141</eissn><abstract>Let ζ( s ) be the Riemann zeta-function. If t ⩾ 6.8 and σ &gt; 1/2, then it is known that the inequality |ζ(1 − s )| &gt; |ζ( s )| is valid except at the zeros of ζ( s ). Here we investigate the Lerch zeta-function L ( λ , α , s ) which usually has many zeros off the critical line and it is expected that these zeros are asymmetrically distributed with respect to the critical line. However, for equal parameters λ = α it is still possible to obtain a certain version of the inequality | L ( λ , λ , 1 − s ¯ )| &gt; | L ( λ , λ , s)|.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.21136/CMJ.2018.0149-17</doi><tpages>13</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0011-4642
ispartof Czechoslovak mathematical journal, 2019-03, Vol.69 (1), p.25-37
issn 0011-4642
1572-9141
language eng
recordid cdi_proquest_journals_2191385609
source Springer Nature - Complete Springer Journals; Alma/SFX Local Collection; EZB Electronic Journals Library
subjects Analysis
Convex and Discrete Geometry
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
title The Size of the Lerch Zeta-Function at Places Symmetric with Respect to the Line ℜ(s) = 1/2
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-22T16%3A24%3A00IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_sprin&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=The%20Size%20of%20the%20Lerch%20Zeta-Function%20at%20Places%20Symmetric%20with%20Respect%20to%20the%20Line%20%E2%84%9C(s)%20=%201/2&rft.jtitle=Czechoslovak%20mathematical%20journal&rft.au=Garunk%C5%A1tis,%20Ram%C5%ABnas&rft.date=2019-03-01&rft.volume=69&rft.issue=1&rft.spage=25&rft.epage=37&rft.pages=25-37&rft.issn=0011-4642&rft.eissn=1572-9141&rft_id=info:doi/10.21136/CMJ.2018.0149-17&rft_dat=%3Cproquest_sprin%3E2191385609%3C/proquest_sprin%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2191385609&rft_id=info:pmid/&rfr_iscdi=true