A still sharper region where π(x) - li(x) is positive

Yannick Saouter; Timothy Trudgian; Patrick Demichel

doi:10.1090/S0025-5718-2015-02930-5

A still sharper region where π(x) - li(x) is positive

Yannick Saouter, Timothy Trudgian, Patrick Demichel

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

Abstract

We consider the least number x for which a change of sign of π(x)-li(x) occurs. First, we consider modifications of Lehman's method that enable us to obtain better estimates of some error terms. Second, we establish a new smaller upper bound for the first x for which the difference is positive. Third, we use numerical computations to improve the final result.

Original language	English
Pages (from-to)	2433-2446
Number of pages	14
Journal	Mathematics of Computation
Volume	84
Issue number	295
DOIs	https://doi.org/10.1090/S0025-5718-2015-02930-5
Publication status	Published - 2015

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title = "A still sharper region where π(x) - li(x) is positive",

abstract = "We consider the least number x for which a change of sign of π(x)-li(x) occurs. First, we consider modifications of Lehman's method that enable us to obtain better estimates of some error terms. Second, we establish a new smaller upper bound for the first x for which the difference is positive. Third, we use numerical computations to improve the final result.",

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AU - Trudgian, Timothy

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N2 - We consider the least number x for which a change of sign of π(x)-li(x) occurs. First, we consider modifications of Lehman's method that enable us to obtain better estimates of some error terms. Second, we establish a new smaller upper bound for the first x for which the difference is positive. Third, we use numerical computations to improve the final result.

AB - We consider the least number x for which a change of sign of π(x)-li(x) occurs. First, we consider modifications of Lehman's method that enable us to obtain better estimates of some error terms. Second, we establish a new smaller upper bound for the first x for which the difference is positive. Third, we use numerical computations to improve the final result.

UR - https://www.scopus.com/pages/publications/84930860192

U2 - 10.1090/S0025-5718-2015-02930-5

DO - 10.1090/S0025-5718-2015-02930-5

M3 - Article

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SP - 2433

EP - 2446

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 295

ER -

A still sharper region where π(x) - li(x) is positive

Abstract

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