Properties of the function f(x)=x/π(x)
We obtain the asymptotic estimations for ∑k=2nf(k) and ∑k=2n1/f(k), where f(k)=k/π(k), k≥2. We study the expression 2f(x+y)−f(x)−f(y) for integers x,y≥2 and as an application we make several remarks in connection with the conjecture of Hardy and Littlewood.
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| Format: | Article |
| Language: | English |
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Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201005725 |
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| _version_ | 1832566650951434240 |
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| author | Panayiotis Vlamos |
| author_facet | Panayiotis Vlamos |
| author_sort | Panayiotis Vlamos |
| collection | DOAJ |
| description | We obtain the asymptotic estimations for ∑k=2nf(k) and ∑k=2n1/f(k), where f(k)=k/π(k), k≥2. We study the expression 2f(x+y)−f(x)−f(y) for integers x,y≥2 and
as an application we make several remarks in connection with the
conjecture of Hardy and Littlewood. |
| format | Article |
| id | doaj-art-e468282d351a45cb90e54192ee0a0538 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e468282d351a45cb90e54192ee0a05382025-02-03T01:03:33ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0128530731110.1155/S0161171201005725Properties of the function f(x)=x/π(x)Panayiotis Vlamos0Hellenic Open University, GreeceWe obtain the asymptotic estimations for ∑k=2nf(k) and ∑k=2n1/f(k), where f(k)=k/π(k), k≥2. We study the expression 2f(x+y)−f(x)−f(y) for integers x,y≥2 and as an application we make several remarks in connection with the conjecture of Hardy and Littlewood.http://dx.doi.org/10.1155/S0161171201005725 |
| spellingShingle | Panayiotis Vlamos Properties of the function f(x)=x/π(x) International Journal of Mathematics and Mathematical Sciences |
| title | Properties of the function f(x)=x/π(x) |
| title_full | Properties of the function f(x)=x/π(x) |
| title_fullStr | Properties of the function f(x)=x/π(x) |
| title_full_unstemmed | Properties of the function f(x)=x/π(x) |
| title_short | Properties of the function f(x)=x/π(x) |
| title_sort | properties of the function f x x π x |
| url | http://dx.doi.org/10.1155/S0161171201005725 |
| work_keys_str_mv | AT panayiotisvlamos propertiesofthefunctionfxxpx |