An analytic method for bounding \psi(x)
In this paper we present an analytic algorithm which calculates almost sharp bounds for the normalized remainder term (t-\psi (t))/\sqrt t for t\leq x in expected run time O(x^{1/2+\varepsilon }) for every \varepsilon >0. The method has been implemented and used to calculate such bounds for t\leq...
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| Veröffentlicht in: | Mathematics of computation 2018-07, Vol.87 (312), p.1991 |
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| container_issue | 312 |
| container_start_page | 1991 |
| container_title | Mathematics of computation |
| container_volume | 87 |
| creator | Jan Büthe |
| description | In this paper we present an analytic algorithm which calculates almost sharp bounds for the normalized remainder term (t-\psi (t))/\sqrt t for t\leq x in expected run time O(x^{1/2+\varepsilon }) for every \varepsilon >0. The method has been implemented and used to calculate such bounds for t\leq 10^{19}. In particular, these imply that li(x)-\pi (x) is positive for 2\leq x\leq 10^{19}. |
| doi_str_mv | 10.1090/mcom/3264 |
| format | Article |
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| fulltext | fulltext |
| identifier | ISSN: 0025-5718 |
| ispartof | Mathematics of computation, 2018-07, Vol.87 (312), p.1991 |
| issn | 0025-5718 1088-6842 |
| language | eng |
| recordid | cdi_ams_primary_10_1090_mcom_3264 |
| source | American Mathematical Society Publications (Freely Accessible); JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; American Mathematical Society Publications |
| title | An analytic method for bounding \psi(x) |
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