Value-Distribution of the Riemann Zeta-Function Along Its Julia Lines
For an arbitrary complex number a ≠ 0 we consider the distribution of values of the Riemann zeta-function ζ at the a -points of the function Δ which appears in the functional equation ζ ( s ) = Δ ( s ) ζ ( 1 - s ) . These a -points δ a are clustered around the critical line 1 / 2 + i R which happens...
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| Veröffentlicht in: | Computational methods and function theory 2020-11, Vol.20 (3-4), p.389-401 |
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| container_title | Computational methods and function theory |
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| creator | Steuding, Jörn Suriajaya, Ade Irma |
| description | For an arbitrary complex number
a
≠
0
we consider the distribution of values of the Riemann zeta-function
ζ
at the
a
-points of the function
Δ
which appears in the functional equation
ζ
(
s
)
=
Δ
(
s
)
ζ
(
1
-
s
)
. These
a
-points
δ
a
are clustered around the critical line
1
/
2
+
i
R
which happens to be a Julia line for the essential singularity of
ζ
at infinity. We observe a remarkable average behaviour for the sequence of values
ζ
(
δ
a
)
. |
| doi_str_mv | 10.1007/s40315-020-00316-x |
| format | Article |
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a
≠
0
we consider the distribution of values of the Riemann zeta-function
ζ
at the
a
-points of the function
Δ
which appears in the functional equation
ζ
(
s
)
=
Δ
(
s
)
ζ
(
1
-
s
)
. These
a
-points
δ
a
are clustered around the critical line
1
/
2
+
i
R
which happens to be a Julia line for the essential singularity of
ζ
at infinity. We observe a remarkable average behaviour for the sequence of values
ζ
(
δ
a
)
.</description><identifier>ISSN: 1617-9447</identifier><identifier>EISSN: 2195-3724</identifier><identifier>DOI: 10.1007/s40315-020-00316-x</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Analysis ; Complex numbers ; Computational Mathematics and Numerical Analysis ; Functional equations ; Functions of a Complex Variable ; Mathematics ; Mathematics and Statistics</subject><ispartof>Computational methods and function theory, 2020-11, Vol.20 (3-4), p.389-401</ispartof><rights>The Author(s) 2020</rights><rights>The Author(s) 2020. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c473t-21f83cfd598d07c953194cb7041675a9875122fa0e9f922b9ef7ec3be309e3aa3</citedby><cites>FETCH-LOGICAL-c473t-21f83cfd598d07c953194cb7041675a9875122fa0e9f922b9ef7ec3be309e3aa3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s40315-020-00316-x$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40315-020-00316-x$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Steuding, Jörn</creatorcontrib><creatorcontrib>Suriajaya, Ade Irma</creatorcontrib><title>Value-Distribution of the Riemann Zeta-Function Along Its Julia Lines</title><title>Computational methods and function theory</title><addtitle>Comput. Methods Funct. Theory</addtitle><description>For an arbitrary complex number
a
≠
0
we consider the distribution of values of the Riemann zeta-function
ζ
at the
a
-points of the function
Δ
which appears in the functional equation
ζ
(
s
)
=
Δ
(
s
)
ζ
(
1
-
s
)
. These
a
-points
δ
a
are clustered around the critical line
1
/
2
+
i
R
which happens to be a Julia line for the essential singularity of
ζ
at infinity. We observe a remarkable average behaviour for the sequence of values
ζ
(
δ
a
)
.</description><subject>Analysis</subject><subject>Complex numbers</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Functional equations</subject><subject>Functions of a Complex Variable</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>1617-9447</issn><issn>2195-3724</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9kMtKAzEUhoMoWKsv4CrgOprbTCbLUttaKQiiLtyETJrUKdNMTTJQ397YEdy5Oj-c_wIfANcE3xKMxV3kmJECYYoRzqpEhxMwokQWiAnKT8GIlEQgybk4BxcxbjEuuGRsBGZvuu0tum9iCk3dp6bzsHMwfVj43Nid9h6-26TRvPfm-Jy0nd_AZYrwsW8bDVeNt_ESnDndRnv1e8fgdT57mT6g1dNiOZ2skOGCJUSJq5hx60JWayyMLBiR3NQCc1KKQstKFIRSp7GVTlJaS-uENay2DEvLtGZjcDP07kP32duY1Lbrg8-TiuYFIXhFyuyig8uELsZgndqHZqfDlyJY_eBSAy6VcakjLnXIITaEYjb7jQ1_1f-kvgHD5Wya</recordid><startdate>20201101</startdate><enddate>20201101</enddate><creator>Steuding, Jörn</creator><creator>Suriajaya, Ade Irma</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20201101</creationdate><title>Value-Distribution of the Riemann Zeta-Function Along Its Julia Lines</title><author>Steuding, Jörn ; Suriajaya, Ade Irma</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c473t-21f83cfd598d07c953194cb7041675a9875122fa0e9f922b9ef7ec3be309e3aa3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Analysis</topic><topic>Complex numbers</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Functional equations</topic><topic>Functions of a Complex Variable</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Steuding, Jörn</creatorcontrib><creatorcontrib>Suriajaya, Ade Irma</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><jtitle>Computational methods and function theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Steuding, Jörn</au><au>Suriajaya, Ade Irma</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Value-Distribution of the Riemann Zeta-Function Along Its Julia Lines</atitle><jtitle>Computational methods and function theory</jtitle><stitle>Comput. Methods Funct. Theory</stitle><date>2020-11-01</date><risdate>2020</risdate><volume>20</volume><issue>3-4</issue><spage>389</spage><epage>401</epage><pages>389-401</pages><issn>1617-9447</issn><eissn>2195-3724</eissn><abstract>For an arbitrary complex number
a
≠
0
we consider the distribution of values of the Riemann zeta-function
ζ
at the
a
-points of the function
Δ
which appears in the functional equation
ζ
(
s
)
=
Δ
(
s
)
ζ
(
1
-
s
)
. These
a
-points
δ
a
are clustered around the critical line
1
/
2
+
i
R
which happens to be a Julia line for the essential singularity of
ζ
at infinity. We observe a remarkable average behaviour for the sequence of values
ζ
(
δ
a
)
.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s40315-020-00316-x</doi><tpages>13</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1617-9447 |
| ispartof | Computational methods and function theory, 2020-11, Vol.20 (3-4), p.389-401 |
| issn | 1617-9447 2195-3724 |
| language | eng |
| recordid | cdi_proquest_journals_2473774816 |
| source | SpringerLink Journals |
| subjects | Analysis Complex numbers Computational Mathematics and Numerical Analysis Functional equations Functions of a Complex Variable Mathematics Mathematics and Statistics |
| title | Value-Distribution of the Riemann Zeta-Function Along Its Julia Lines |
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