CONVOLUTION FORMULA AS A STIELTJES RESULTANT
In pursuit of the number-theoretic nature of a given set, one defines an arithmetic function and considers its average behavior in view of the fact that independent values are rather singular. We are interested in the asymptotic formula for the summatory function of an arithmetic function which is g...
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| Veröffentlicht in: | Kyushu Journal of Mathematics 2018, Vol.72(2), pp.429-439 |
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| container_title | Kyushu Journal of Mathematics |
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| creator | BANERJEE, Soumyarup KANEMITSU, Shigeru |
| description | In pursuit of the number-theoretic nature of a given set, one defines an arithmetic function and considers its average behavior in view of the fact that independent values are rather singular. We are interested in the asymptotic formula for the summatory function of an arithmetic function which is given as the coefficients of the product of two generating Dirichlet series, i.e. they are convolutions of the respective coefficients. Our main purpose is to elucidate the far-reaching theorem of Lau in the light of the Stieltjes resultant and to give some applications which involve possible logarithmic singularities. |
| doi_str_mv | 10.2206/kyushujm.72.429 |
| format | Article |
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We are interested in the asymptotic formula for the summatory function of an arithmetic function which is given as the coefficients of the product of two generating Dirichlet series, i.e. they are convolutions of the respective coefficients. Our main purpose is to elucidate the far-reaching theorem of Lau in the light of the Stieltjes resultant and to give some applications which involve possible logarithmic singularities.</description><identifier>ISSN: 1340-6116</identifier><identifier>EISSN: 1883-2032</identifier><identifier>DOI: 10.2206/kyushujm.72.429</identifier><language>eng</language><publisher>Hukuoka: Faculty of Mathematics, Kyushu University</publisher><subject>Arithmetic ; asymptotic formula ; Convolution ; Dirichlet convolution ; Dirichlet problem ; generating Dirichlet series ; Mathematical functions ; Singularity (mathematics) ; Stieltjes resultant</subject><ispartof>Kyushu Journal of Mathematics, 2018, Vol.72(2), pp.429-439</ispartof><rights>2018 Faculty of Mathematics, Kyushu University</rights><rights>Copyright Japan Science and Technology Agency 2018</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c449t-3d2260b1772f082c7886fefef6e6c3ded8620e69059d6ac9fe64038fddd49ad03</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,1877,4010,27900,27901,27902</link.rule.ids></links><search><creatorcontrib>BANERJEE, Soumyarup</creatorcontrib><creatorcontrib>KANEMITSU, Shigeru</creatorcontrib><title>CONVOLUTION FORMULA AS A STIELTJES RESULTANT</title><title>Kyushu Journal of Mathematics</title><addtitle>Kyushu J. Math.</addtitle><description>In pursuit of the number-theoretic nature of a given set, one defines an arithmetic function and considers its average behavior in view of the fact that independent values are rather singular. We are interested in the asymptotic formula for the summatory function of an arithmetic function which is given as the coefficients of the product of two generating Dirichlet series, i.e. they are convolutions of the respective coefficients. Our main purpose is to elucidate the far-reaching theorem of Lau in the light of the Stieltjes resultant and to give some applications which involve possible logarithmic singularities.</description><subject>Arithmetic</subject><subject>asymptotic formula</subject><subject>Convolution</subject><subject>Dirichlet convolution</subject><subject>Dirichlet problem</subject><subject>generating Dirichlet series</subject><subject>Mathematical functions</subject><subject>Singularity (mathematics)</subject><subject>Stieltjes resultant</subject><issn>1340-6116</issn><issn>1883-2032</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNpVkE1PwzAMhiMEEmNw5lqJK90Sp0vTY5m6MVRWaW25RiFJ2cq-SNrD_j2dNiYhH2zJz2tLD0KPBA8AMBt-H1q3bOvNIIRBANEV6hHOqQ-YwnU30wD7jBB2i-6cqzGmjAPtoedxNv_I0rKYZXNvki3eyzT24tyLvbyYJWnxluTeIsnLtIjnxT26qeTamYdz76NykhTjVz_NprNxnPoqCKLGpxqA4U8ShlBhDirknFWmK2aYotpozgAbFuFRpJlUUWVYgCmvtNZBJDWmffR0uru3u5_WuEbUu9Zuu5cCgI5CQkJ6pIYnStmdc9ZUYm9XG2kPgmBxVCL-lIgQRKekS7ycErVr5Je58NI2K7U2_3g4hy5LtZRWmC39BbBuamY</recordid><startdate>2018</startdate><enddate>2018</enddate><creator>BANERJEE, Soumyarup</creator><creator>KANEMITSU, Shigeru</creator><general>Faculty of Mathematics, Kyushu University</general><general>Japan Science and Technology Agency</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>2018</creationdate><title>CONVOLUTION FORMULA AS A STIELTJES RESULTANT</title><author>BANERJEE, Soumyarup ; KANEMITSU, Shigeru</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c449t-3d2260b1772f082c7886fefef6e6c3ded8620e69059d6ac9fe64038fddd49ad03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Arithmetic</topic><topic>asymptotic formula</topic><topic>Convolution</topic><topic>Dirichlet convolution</topic><topic>Dirichlet problem</topic><topic>generating Dirichlet series</topic><topic>Mathematical functions</topic><topic>Singularity (mathematics)</topic><topic>Stieltjes resultant</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>BANERJEE, Soumyarup</creatorcontrib><creatorcontrib>KANEMITSU, Shigeru</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Kyushu Journal of Mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>BANERJEE, Soumyarup</au><au>KANEMITSU, Shigeru</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>CONVOLUTION FORMULA AS A STIELTJES RESULTANT</atitle><jtitle>Kyushu Journal of Mathematics</jtitle><addtitle>Kyushu J. 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| ispartof | Kyushu Journal of Mathematics, 2018, Vol.72(2), pp.429-439 |
| issn | 1340-6116 1883-2032 |
| language | eng |
| recordid | cdi_proquest_journals_2235711730 |
| source | J-STAGE Free; EZB-FREE-00999 freely available EZB journals |
| subjects | Arithmetic asymptotic formula Convolution Dirichlet convolution Dirichlet problem generating Dirichlet series Mathematical functions Singularity (mathematics) Stieltjes resultant |
| title | CONVOLUTION FORMULA AS A STIELTJES RESULTANT |
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