Estimates of convolutions of certain number-theoretic error terms
Several estimates for the convolution function C [f(x)]:=∫1xf(y) f(x/y)(dy/y) and its iterates are obtained when f(x) is a suitable number-theoretic error term. We deal with the case of the asymptotic formula for ∫0T|ζ(1/2+it)|2kdt(k=1,2), the general Dirichlet divisor problem, the problem of noniso...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204305156 |
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| _version_ | 1849402751486787584 |
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| author | Aleksandar Ivic |
| author_facet | Aleksandar Ivic |
| author_sort | Aleksandar Ivic |
| collection | DOAJ |
| description | Several estimates for the convolution function C [f(x)]:=∫1xf(y) f(x/y)(dy/y) and its iterates are obtained when f(x) is a suitable number-theoretic error term. We deal with the case of the asymptotic formula for ∫0T|ζ(1/2+it)|2kdt(k=1,2), the general Dirichlet divisor problem, the problem of nonisomorphic Abelian groups of given order, and the Rankin-Selberg convolution. |
| format | Article |
| id | doaj-art-94770b74ef95482aa9da97480fb80331 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-94770b74ef95482aa9da97480fb803312025-08-20T03:37:28ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004112310.1155/S0161171204305156Estimates of convolutions of certain number-theoretic error termsAleksandar Ivic0Katedra Matematike RGF-a, Universiteta u Beogradu, Ðušina 7, Beograd 11000, Serbia and MontenegroSeveral estimates for the convolution function C [f(x)]:=∫1xf(y) f(x/y)(dy/y) and its iterates are obtained when f(x) is a suitable number-theoretic error term. We deal with the case of the asymptotic formula for ∫0T|ζ(1/2+it)|2kdt(k=1,2), the general Dirichlet divisor problem, the problem of nonisomorphic Abelian groups of given order, and the Rankin-Selberg convolution.http://dx.doi.org/10.1155/S0161171204305156 |
| spellingShingle | Aleksandar Ivic Estimates of convolutions of certain number-theoretic error terms International Journal of Mathematics and Mathematical Sciences |
| title | Estimates of convolutions of certain number-theoretic error terms |
| title_full | Estimates of convolutions of certain number-theoretic error terms |
| title_fullStr | Estimates of convolutions of certain number-theoretic error terms |
| title_full_unstemmed | Estimates of convolutions of certain number-theoretic error terms |
| title_short | Estimates of convolutions of certain number-theoretic error terms |
| title_sort | estimates of convolutions of certain number theoretic error terms |
| url | http://dx.doi.org/10.1155/S0161171204305156 |
| work_keys_str_mv | AT aleksandarivic estimatesofconvolutionsofcertainnumbertheoreticerrorterms |