On I<q- and I≤q-convergence of arithmetic functions
Let N be the set of positive integers, and denote by λ ( A ) = inf { t > 0 : ∑ a ∈ A a - t < ∞ } the convergence exponent of A ⊂ N . For 0 < q ≤ 1 , 0 ≤ q ≤ 1 , respectively, the admissible ideals I < q , I ≤ q of all subsets A ⊂ N with λ ( A ) < q , λ ( A ) ≤ q , respectively, satisf...
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| Veröffentlicht in: | Periodica mathematica Hungarica 2021-06, Vol.82 (2), p.125-135 |
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| creator | Tóth, János T. Filip, Ferdinánd Bukor, József Zsilinszky, László |
| description | Let
N
be the set of positive integers, and denote by
λ
(
A
)
=
inf
{
t
>
0
:
∑
a
∈
A
a
-
t
<
∞
}
the convergence exponent of
A
⊂
N
. For
0
<
q
≤
1
,
0
≤
q
≤
1
, respectively, the admissible ideals
I
<
q
,
I
≤
q
of all subsets
A
⊂
N
with
λ
(
A
)
<
q
,
λ
(
A
)
≤
q
, respectively, satisfy
I
<
q
⊊
I
c
(
q
)
⊊
I
≤
q
, where
I
c
(
q
)
=
{
A
⊂
N
:
∑
a
∈
A
a
-
q
<
∞
}
.
In this note we sharpen the results of Baláž et al. from (J Number Theory 183:74–83, 2018) and other papers, concerning characterizations of
I
c
(
q
)
-convergence of various arithmetic functions in terms of
q
. This is achieved by utilizing
I
<
q
- and
I
≤
q
-convergence, for which new methods and criteria are developed. |
| doi_str_mv | 10.1007/s10998-020-00345-y |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_sprin</sourceid><recordid>TN_cdi_proquest_journals_2528474770</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2528474770</sourcerecordid><originalsourceid>FETCH-LOGICAL-p227t-84cdb4114dbc1b35bc76d1595f60147d213a0b21046ef3f9ae3549a447e4834e3</originalsourceid><addsrcrecordid>eNpFkNFKwzAUhoMoOKcv4FXB6-g5ycmSgDcydA4Gu9Hr0Kbp7NC0a1phj-B7-GQ-idUJXh34-f7_wMfYJcI1AuibhGCt4SCAA0hSfH_EJqiM4cIIe8wmY4pcSZCn7CylLcBYkzBhah2z5e2OZ3kss-XXx-eO-ya-h24Tog9ZU2V5V_cvb6GvfVYN0fd1E9M5O6ny1xQu_u6UPT_cP80f-Wq9WM7vVrwVQvfckC8LQqSy8FhIVXg9K1FZVc0ASZcCZQ6FQKBZqGRl8yAV2ZxIBzKSgpyyq8Nu2zW7IaTebZuhi-NLJ5QwpElrGCl5oFLb1XETun8Kwf34cQc_bvTjfv24vfwGslNXpA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2528474770</pqid></control><display><type>article</type><title>On I<q- and I≤q-convergence of arithmetic functions</title><source>SpringerLink Journals - AutoHoldings</source><creator>Tóth, János T. ; Filip, Ferdinánd ; Bukor, József ; Zsilinszky, László</creator><creatorcontrib>Tóth, János T. ; Filip, Ferdinánd ; Bukor, József ; Zsilinszky, László</creatorcontrib><description><![CDATA[Let
N
be the set of positive integers, and denote by
λ
(
A
)
=
inf
{
t
>
0
:
∑
a
∈
A
a
-
t
<
∞
}
the convergence exponent of
A
⊂
N
. For
0
<
q
≤
1
,
0
≤
q
≤
1
, respectively, the admissible ideals
I
<
q
,
I
≤
q
of all subsets
A
⊂
N
with
λ
(
A
)
<
q
,
λ
(
A
)
≤
q
, respectively, satisfy
I
<
q
⊊
I
c
(
q
)
⊊
I
≤
q
, where
I
c
(
q
)
=
{
A
⊂
N
:
∑
a
∈
A
a
-
q
<
∞
}
.
In this note we sharpen the results of Baláž et al. from (J Number Theory 183:74–83, 2018) and other papers, concerning characterizations of
I
c
(
q
)
-convergence of various arithmetic functions in terms of
q
. This is achieved by utilizing
I
<
q
- and
I
≤
q
-convergence, for which new methods and criteria are developed.]]></description><identifier>ISSN: 0031-5303</identifier><identifier>EISSN: 1588-2829</identifier><identifier>DOI: 10.1007/s10998-020-00345-y</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Arithmetic ; Convergence ; Mathematical functions ; Mathematics ; Mathematics and Statistics ; Number theory</subject><ispartof>Periodica mathematica Hungarica, 2021-06, Vol.82 (2), p.125-135</ispartof><rights>Akadémiai Kiadó, Budapest, Hungary 2020</rights><rights>Akadémiai Kiadó, Budapest, Hungary 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-p227t-84cdb4114dbc1b35bc76d1595f60147d213a0b21046ef3f9ae3549a447e4834e3</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/s10998-020-00345-y$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10998-020-00345-y$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Tóth, János T.</creatorcontrib><creatorcontrib>Filip, Ferdinánd</creatorcontrib><creatorcontrib>Bukor, József</creatorcontrib><creatorcontrib>Zsilinszky, László</creatorcontrib><title>On I<q- and I≤q-convergence of arithmetic functions</title><title>Periodica mathematica Hungarica</title><addtitle>Period Math Hung</addtitle><description><![CDATA[Let
N
be the set of positive integers, and denote by
λ
(
A
)
=
inf
{
t
>
0
:
∑
a
∈
A
a
-
t
<
∞
}
the convergence exponent of
A
⊂
N
. For
0
<
q
≤
1
,
0
≤
q
≤
1
, respectively, the admissible ideals
I
<
q
,
I
≤
q
of all subsets
A
⊂
N
with
λ
(
A
)
<
q
,
λ
(
A
)
≤
q
, respectively, satisfy
I
<
q
⊊
I
c
(
q
)
⊊
I
≤
q
, where
I
c
(
q
)
=
{
A
⊂
N
:
∑
a
∈
A
a
-
q
<
∞
}
.
In this note we sharpen the results of Baláž et al. from (J Number Theory 183:74–83, 2018) and other papers, concerning characterizations of
I
c
(
q
)
-convergence of various arithmetic functions in terms of
q
. This is achieved by utilizing
I
<
q
- and
I
≤
q
-convergence, for which new methods and criteria are developed.]]></description><subject>Arithmetic</subject><subject>Convergence</subject><subject>Mathematical functions</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Number theory</subject><issn>0031-5303</issn><issn>1588-2829</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNpFkNFKwzAUhoMoOKcv4FXB6-g5ycmSgDcydA4Gu9Hr0Kbp7NC0a1phj-B7-GQ-idUJXh34-f7_wMfYJcI1AuibhGCt4SCAA0hSfH_EJqiM4cIIe8wmY4pcSZCn7CylLcBYkzBhah2z5e2OZ3kss-XXx-eO-ya-h24Tog9ZU2V5V_cvb6GvfVYN0fd1E9M5O6ny1xQu_u6UPT_cP80f-Wq9WM7vVrwVQvfckC8LQqSy8FhIVXg9K1FZVc0ASZcCZQ6FQKBZqGRl8yAV2ZxIBzKSgpyyq8Nu2zW7IaTebZuhi-NLJ5QwpElrGCl5oFLb1XETun8Kwf34cQc_bvTjfv24vfwGslNXpA</recordid><startdate>20210601</startdate><enddate>20210601</enddate><creator>Tóth, János T.</creator><creator>Filip, Ferdinánd</creator><creator>Bukor, József</creator><creator>Zsilinszky, László</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope/></search><sort><creationdate>20210601</creationdate><title>On I<q- and I≤q-convergence of arithmetic functions</title><author>Tóth, János T. ; Filip, Ferdinánd ; Bukor, József ; Zsilinszky, László</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p227t-84cdb4114dbc1b35bc76d1595f60147d213a0b21046ef3f9ae3549a447e4834e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Arithmetic</topic><topic>Convergence</topic><topic>Mathematical functions</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Number theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Tóth, János T.</creatorcontrib><creatorcontrib>Filip, Ferdinánd</creatorcontrib><creatorcontrib>Bukor, József</creatorcontrib><creatorcontrib>Zsilinszky, László</creatorcontrib><jtitle>Periodica mathematica Hungarica</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Tóth, János T.</au><au>Filip, Ferdinánd</au><au>Bukor, József</au><au>Zsilinszky, László</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On I<q- and I≤q-convergence of arithmetic functions</atitle><jtitle>Periodica mathematica Hungarica</jtitle><stitle>Period Math Hung</stitle><date>2021-06-01</date><risdate>2021</risdate><volume>82</volume><issue>2</issue><spage>125</spage><epage>135</epage><pages>125-135</pages><issn>0031-5303</issn><eissn>1588-2829</eissn><abstract><![CDATA[Let
N
be the set of positive integers, and denote by
λ
(
A
)
=
inf
{
t
>
0
:
∑
a
∈
A
a
-
t
<
∞
}
the convergence exponent of
A
⊂
N
. For
0
<
q
≤
1
,
0
≤
q
≤
1
, respectively, the admissible ideals
I
<
q
,
I
≤
q
of all subsets
A
⊂
N
with
λ
(
A
)
<
q
,
λ
(
A
)
≤
q
, respectively, satisfy
I
<
q
⊊
I
c
(
q
)
⊊
I
≤
q
, where
I
c
(
q
)
=
{
A
⊂
N
:
∑
a
∈
A
a
-
q
<
∞
}
.
In this note we sharpen the results of Baláž et al. from (J Number Theory 183:74–83, 2018) and other papers, concerning characterizations of
I
c
(
q
)
-convergence of various arithmetic functions in terms of
q
. This is achieved by utilizing
I
<
q
- and
I
≤
q
-convergence, for which new methods and criteria are developed.]]></abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s10998-020-00345-y</doi><tpages>11</tpages></addata></record> |
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| ispartof | Periodica mathematica Hungarica, 2021-06, Vol.82 (2), p.125-135 |
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| language | eng |
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| subjects | Arithmetic Convergence Mathematical functions Mathematics Mathematics and Statistics Number theory |
| title | On I<q- and I≤q-convergence of arithmetic functions |
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