A GL3 analog of Selberg’s result on S(t)
Let S ( t , F ) : = π - 1 arg L ( 1 2 + i t , F ) , where F is a Hecke–Maass cusp form for SL 3 ( Z ) . We establish an asymptotic formula for the spectral moments of S ( t , F ), and obtain several other results on S ( t , F ).
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| Veröffentlicht in: | The Ramanujan journal 2021, Vol.56 (1), p.163-181 |
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| container_title | The Ramanujan journal |
| container_volume | 56 |
| creator | Liu, Sheng-Chi Liu, Shenhui |
| description | Let
S
(
t
,
F
)
:
=
π
-
1
arg
L
(
1
2
+
i
t
,
F
)
,
where
F
is a Hecke–Maass cusp form for
SL
3
(
Z
)
.
We establish an asymptotic formula for the spectral moments of
S
(
t
,
F
), and obtain several other results on
S
(
t
,
F
). |
| doi_str_mv | 10.1007/s11139-020-00308-4 |
| format | Article |
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S
(
t
,
F
)
:
=
π
-
1
arg
L
(
1
2
+
i
t
,
F
)
,
where
F
is a Hecke–Maass cusp form for
SL
3
(
Z
)
.
We establish an asymptotic formula for the spectral moments of
S
(
t
,
F
), and obtain several other results on
S
(
t
,
F
).</description><identifier>ISSN: 1382-4090</identifier><identifier>EISSN: 1572-9303</identifier><identifier>DOI: 10.1007/s11139-020-00308-4</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Combinatorics ; Field Theory and Polynomials ; Fourier Analysis ; Functions of a Complex Variable ; Mathematics ; Mathematics and Statistics ; Number Theory</subject><ispartof>The Ramanujan journal, 2021, Vol.56 (1), p.163-181</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2020</rights><rights>Springer Science+Business Media, LLC, part of Springer Nature 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-p157t-3bcc1a5d8dd4508f0276bea61368bd163357ef76734111d327288f9c7df1a44e3</cites><orcidid>0000-0002-8560-4772</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11139-020-00308-4$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11139-020-00308-4$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Liu, Sheng-Chi</creatorcontrib><creatorcontrib>Liu, Shenhui</creatorcontrib><title>A GL3 analog of Selberg’s result on S(t)</title><title>The Ramanujan journal</title><addtitle>Ramanujan J</addtitle><description>Let
S
(
t
,
F
)
:
=
π
-
1
arg
L
(
1
2
+
i
t
,
F
)
,
where
F
is a Hecke–Maass cusp form for
SL
3
(
Z
)
.
We establish an asymptotic formula for the spectral moments of
S
(
t
,
F
), and obtain several other results on
S
(
t
,
F
).</description><subject>Combinatorics</subject><subject>Field Theory and Polynomials</subject><subject>Fourier Analysis</subject><subject>Functions of a Complex Variable</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Number Theory</subject><issn>1382-4090</issn><issn>1572-9303</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNpFkMFKxDAQhoMouK6-gKeAFxWik0zSpMdlWVeh4GH1HNomLS6lrUl79zV8PZ_E6AqeZg4f__zzEXLJ4Y4D6PvIOcecgQAGgGCYPCILrrRgOQIepx2NYBJyOCVnMe4BQALqBbld0W2BtOzLbmjp0NCd7yof2q-Pz0iDj3M30aGnu-vp5pycNGUX_cXfXJLXh83L-pEVz9un9apgYzo4MazqmpfKGeekAtOA0Fnly4xjZirHM0SlfaMzjTKVdii0MKbJa-0aXkrpcUmuDrljGN5nHye7H-aQCkYr0kdCcVAmUXig4hje-taHf4qD_ZFiD1JskmJ_pViJ3_8RUc8</recordid><startdate>2021</startdate><enddate>2021</enddate><creator>Liu, Sheng-Chi</creator><creator>Liu, Shenhui</creator><general>Springer US</general><general>Springer Nature B.V</general><scope/><orcidid>https://orcid.org/0000-0002-8560-4772</orcidid></search><sort><creationdate>2021</creationdate><title>A GL3 analog of Selberg’s result on S(t)</title><author>Liu, Sheng-Chi ; Liu, Shenhui</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p157t-3bcc1a5d8dd4508f0276bea61368bd163357ef76734111d327288f9c7df1a44e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Combinatorics</topic><topic>Field Theory and Polynomials</topic><topic>Fourier Analysis</topic><topic>Functions of a Complex Variable</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Number Theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liu, Sheng-Chi</creatorcontrib><creatorcontrib>Liu, Shenhui</creatorcontrib><jtitle>The Ramanujan journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Liu, Sheng-Chi</au><au>Liu, Shenhui</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A GL3 analog of Selberg’s result on S(t)</atitle><jtitle>The Ramanujan journal</jtitle><stitle>Ramanujan J</stitle><date>2021</date><risdate>2021</risdate><volume>56</volume><issue>1</issue><spage>163</spage><epage>181</epage><pages>163-181</pages><issn>1382-4090</issn><eissn>1572-9303</eissn><abstract>Let
S
(
t
,
F
)
:
=
π
-
1
arg
L
(
1
2
+
i
t
,
F
)
,
where
F
is a Hecke–Maass cusp form for
SL
3
(
Z
)
.
We establish an asymptotic formula for the spectral moments of
S
(
t
,
F
), and obtain several other results on
S
(
t
,
F
).</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11139-020-00308-4</doi><tpages>19</tpages><orcidid>https://orcid.org/0000-0002-8560-4772</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1382-4090 |
| ispartof | The Ramanujan journal, 2021, Vol.56 (1), p.163-181 |
| issn | 1382-4090 1572-9303 |
| language | eng |
| recordid | cdi_proquest_journals_2572251058 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Combinatorics Field Theory and Polynomials Fourier Analysis Functions of a Complex Variable Mathematics Mathematics and Statistics Number Theory |
| title | A GL3 analog of Selberg’s result on S(t) |
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