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...
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Veröffentlicht in: | Czechoslovak mathematical journal 2019-03, Vol.69 (1), p.25-37 |
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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 |
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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)|.</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
> 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)|.</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
> 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)|.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.21136/CMJ.2018.0149-17</doi><tpages>13</tpages></addata></record> |
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issn | 0011-4642 1572-9141 |
language | eng |
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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 |
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