Estimates for lattice points of quadratic forms with integral coefficients modulo a prime number square
Let be a nonsingular quadratic form with integer coefficients, n be even. Let V = V Q = V p 2 denote the set of zeros of Q ( x ) in Z p 2 , p be an odd prime, and | V | denote the cardinality of V . In this paper, we are interested in giving an upper bound of the number of integer solutions of the...
Gespeichert in:
| Veröffentlicht in: | Journal of inequalities and applications 2014-08, Vol.2014 (1), p.1-11, Article 290 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 11 |
|---|---|
| container_issue | 1 |
| container_start_page | 1 |
| container_title | Journal of inequalities and applications |
| container_volume | 2014 |
| creator | Hakami, Ali H |
| description | Let
be a nonsingular quadratic form with integer coefficients,
n
be even. Let
V
=
V
Q
=
V
p
2
denote the set of zeros of
Q
(
x
)
in
Z
p
2
,
p
be an odd prime, and
|
V
|
denote the cardinality of
V
. In this paper, we are interested in giving an upper bound of the number of integer solutions of the congruence
Q
(
x
)
≡
0
(
mod
p
2
)
in small boxes of the type
{
x
∈
Z
p
2
n
|
a
i
⩽
x
i
<
a
i
+
m
i
,
1
⩽
i
⩽
n
}
centered about the origin, where
a
i
,
m
i
∈
Z
, and
0
<
m
i
<
p
2
for
1
⩽
i
⩽
n
.
MSC:
11E04, 11E08, 11E12, 11P21. |
| doi_str_mv | 10.1186/1029-242X-2014-290 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1730065729</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3823315201</sourcerecordid><originalsourceid>FETCH-LOGICAL-c347t-e760610a65b9a459bb3eefa9603a2e4ed2dc54dd2f4aa51a83e190eef2e251de3</originalsourceid><addsrcrecordid>eNp1kMtKAzEUhoMoWC8v4Crgxs1obnNbSqkXKLhRcBdOZ05qysykTTKIb2-GihTBVcI53_-TfIRccXbLeVXccSbqTCjxngnGVSZqdkRmv8Pjg_spOQthw5jgslIzsl6EaHuIGKhxnnYQo22Qbp0dYqDO0N0IrYc0nPZ9oJ82ftC0xLWHjjYOjbGNxYnuXTt2jgLdetsjHcZ-hZ6G1ODxgpwY6AJe_pzn5O1h8Tp_ypYvj8_z-2XWSFXGDMuCFZxBka9qUHm9WklEA3XBJAhU2Iq2yVXbCqMAcg6VRF6zhAgUOW9RnpObfe_Wu92IIerehga7DgZ0Y9C8lIwVeSnqhF7_QTdu9EN6XaJ4xXnBqjJRYk813oXg0ejpd-C_NGd6cq8ntXpSqyf3OrlPIbkPhQQPa_QH1f-nvgF6S4im</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1718116087</pqid></control><display><type>article</type><title>Estimates for lattice points of quadratic forms with integral coefficients modulo a prime number square</title><source>DOAJ Directory of Open Access Journals</source><source>SpringerNature Journals</source><source>Springer Nature OA Free Journals</source><source>EZB-FREE-00999 freely available EZB journals</source><creator>Hakami, Ali H</creator><creatorcontrib>Hakami, Ali H</creatorcontrib><description>Let
be a nonsingular quadratic form with integer coefficients,
n
be even. Let
V
=
V
Q
=
V
p
2
denote the set of zeros of
Q
(
x
)
in
Z
p
2
,
p
be an odd prime, and
|
V
|
denote the cardinality of
V
. In this paper, we are interested in giving an upper bound of the number of integer solutions of the congruence
Q
(
x
)
≡
0
(
mod
p
2
)
in small boxes of the type
{
x
∈
Z
p
2
n
|
a
i
⩽
x
i
<
a
i
+
m
i
,
1
⩽
i
⩽
n
}
centered about the origin, where
a
i
,
m
i
∈
Z
, and
0
<
m
i
<
p
2
for
1
⩽
i
⩽
n
.
MSC:
11E04, 11E08, 11E12, 11P21.</description><identifier>ISSN: 1029-242X</identifier><identifier>ISSN: 1025-5834</identifier><identifier>EISSN: 1029-242X</identifier><identifier>DOI: 10.1186/1029-242X-2014-290</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Analysis ; Applications of Mathematics ; Estimates ; Inequalities ; Integers ; Lattices ; Mathematics ; Mathematics and Statistics ; Origins ; Prime numbers ; Quadratic forms ; Upper bounds</subject><ispartof>Journal of inequalities and applications, 2014-08, Vol.2014 (1), p.1-11, Article 290</ispartof><rights>Hakami; licensee Springer. 2014. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.</rights><rights>The Author(s) 2014</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c347t-e760610a65b9a459bb3eefa9603a2e4ed2dc54dd2f4aa51a83e190eef2e251de3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1186/1029-242X-2014-290$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1186/1029-242X-2014-290$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,864,27924,27925,41120,41488,42189,42557,51319,51576</link.rule.ids></links><search><creatorcontrib>Hakami, Ali H</creatorcontrib><title>Estimates for lattice points of quadratic forms with integral coefficients modulo a prime number square</title><title>Journal of inequalities and applications</title><addtitle>J Inequal Appl</addtitle><description>Let
be a nonsingular quadratic form with integer coefficients,
n
be even. Let
V
=
V
Q
=
V
p
2
denote the set of zeros of
Q
(
x
)
in
Z
p
2
,
p
be an odd prime, and
|
V
|
denote the cardinality of
V
. In this paper, we are interested in giving an upper bound of the number of integer solutions of the congruence
Q
(
x
)
≡
0
(
mod
p
2
)
in small boxes of the type
{
x
∈
Z
p
2
n
|
a
i
⩽
x
i
<
a
i
+
m
i
,
1
⩽
i
⩽
n
}
centered about the origin, where
a
i
,
m
i
∈
Z
, and
0
<
m
i
<
p
2
for
1
⩽
i
⩽
n
.
MSC:
11E04, 11E08, 11E12, 11P21.</description><subject>Analysis</subject><subject>Applications of Mathematics</subject><subject>Estimates</subject><subject>Inequalities</subject><subject>Integers</subject><subject>Lattices</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Origins</subject><subject>Prime numbers</subject><subject>Quadratic forms</subject><subject>Upper bounds</subject><issn>1029-242X</issn><issn>1025-5834</issn><issn>1029-242X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp1kMtKAzEUhoMoWC8v4Crgxs1obnNbSqkXKLhRcBdOZ05qysykTTKIb2-GihTBVcI53_-TfIRccXbLeVXccSbqTCjxngnGVSZqdkRmv8Pjg_spOQthw5jgslIzsl6EaHuIGKhxnnYQo22Qbp0dYqDO0N0IrYc0nPZ9oJ82ftC0xLWHjjYOjbGNxYnuXTt2jgLdetsjHcZ-hZ6G1ODxgpwY6AJe_pzn5O1h8Tp_ypYvj8_z-2XWSFXGDMuCFZxBka9qUHm9WklEA3XBJAhU2Iq2yVXbCqMAcg6VRF6zhAgUOW9RnpObfe_Wu92IIerehga7DgZ0Y9C8lIwVeSnqhF7_QTdu9EN6XaJ4xXnBqjJRYk813oXg0ejpd-C_NGd6cq8ntXpSqyf3OrlPIbkPhQQPa_QH1f-nvgF6S4im</recordid><startdate>20140818</startdate><enddate>20140818</enddate><creator>Hakami, Ali H</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20140818</creationdate><title>Estimates for lattice points of quadratic forms with integral coefficients modulo a prime number square</title><author>Hakami, Ali H</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c347t-e760610a65b9a459bb3eefa9603a2e4ed2dc54dd2f4aa51a83e190eef2e251de3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Analysis</topic><topic>Applications of Mathematics</topic><topic>Estimates</topic><topic>Inequalities</topic><topic>Integers</topic><topic>Lattices</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Origins</topic><topic>Prime numbers</topic><topic>Quadratic forms</topic><topic>Upper bounds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hakami, Ali H</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><jtitle>Journal of inequalities and applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hakami, Ali H</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Estimates for lattice points of quadratic forms with integral coefficients modulo a prime number square</atitle><jtitle>Journal of inequalities and applications</jtitle><stitle>J Inequal Appl</stitle><date>2014-08-18</date><risdate>2014</risdate><volume>2014</volume><issue>1</issue><spage>1</spage><epage>11</epage><pages>1-11</pages><artnum>290</artnum><issn>1029-242X</issn><issn>1025-5834</issn><eissn>1029-242X</eissn><abstract>Let
be a nonsingular quadratic form with integer coefficients,
n
be even. Let
V
=
V
Q
=
V
p
2
denote the set of zeros of
Q
(
x
)
in
Z
p
2
,
p
be an odd prime, and
|
V
|
denote the cardinality of
V
. In this paper, we are interested in giving an upper bound of the number of integer solutions of the congruence
Q
(
x
)
≡
0
(
mod
p
2
)
in small boxes of the type
{
x
∈
Z
p
2
n
|
a
i
⩽
x
i
<
a
i
+
m
i
,
1
⩽
i
⩽
n
}
centered about the origin, where
a
i
,
m
i
∈
Z
, and
0
<
m
i
<
p
2
for
1
⩽
i
⩽
n
.
MSC:
11E04, 11E08, 11E12, 11P21.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1186/1029-242X-2014-290</doi><tpages>11</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1029-242X |
| ispartof | Journal of inequalities and applications, 2014-08, Vol.2014 (1), p.1-11, Article 290 |
| issn | 1029-242X 1025-5834 1029-242X |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1730065729 |
| source | DOAJ Directory of Open Access Journals; SpringerNature Journals; Springer Nature OA Free Journals; EZB-FREE-00999 freely available EZB journals |
| subjects | Analysis Applications of Mathematics Estimates Inequalities Integers Lattices Mathematics Mathematics and Statistics Origins Prime numbers Quadratic forms Upper bounds |
| title | Estimates for lattice points of quadratic forms with integral coefficients modulo a prime number square |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-21T17%3A02%3A18IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Estimates%20for%20lattice%20points%20of%20quadratic%20forms%20with%20integral%20coefficients%20modulo%20a%20prime%20number%20square&rft.jtitle=Journal%20of%20inequalities%20and%20applications&rft.au=Hakami,%20Ali%20H&rft.date=2014-08-18&rft.volume=2014&rft.issue=1&rft.spage=1&rft.epage=11&rft.pages=1-11&rft.artnum=290&rft.issn=1029-242X&rft.eissn=1029-242X&rft_id=info:doi/10.1186/1029-242X-2014-290&rft_dat=%3Cproquest_cross%3E3823315201%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1718116087&rft_id=info:pmid/&rfr_iscdi=true |