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ERROR ESTIMATES FOR A CLASS OF CONTINUOUS BONSE-TYPE INEQUALITIES

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F22%3A50019268" target="_blank" >RIV/62690094:18470/22:50019268 - isvavai.cz</a>

  • Result on the web

    <a href="https://www.ams.org/journals/mcom/2022-91-337/S0025-5718-2022-03741-8/" target="_blank" >https://www.ams.org/journals/mcom/2022-91-337/S0025-5718-2022-03741-8/</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1090/mcom/3741" target="_blank" >10.1090/mcom/3741</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    ERROR ESTIMATES FOR A CLASS OF CONTINUOUS BONSE-TYPE INEQUALITIES

  • Original language description

    Let p(n) be the nth prime number. In 2000, Papaitopol proved that the inequality p(1)... p(n) &gt; p(n+1)(n-pi(n)) holds, for all n &gt;= 2, where pi(x) is the prime counting function. In 2021, Yang and Liao tried to sharpen this inequality by replacing n - pi(n) by n - pi(n) + pi(n)/pi(logn) - 2 pi(pi(n)), however there is a small mistake in their argument. In this paper, we exploit properties of the logarithm error term in inequalities of the type p(1) ... p(n) &gt; p(n+1)(k(n, x)), where k(n, x) = n - pi(n) +pi(n)/pi(logn) - x pi(pi(n)). In particular, we improve Yang and Liao estimate, by showing that the previous inequality at x = 1.4 holds for all n &gt;= 21.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10101 - Pure mathematics

Result continuities

  • Project

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2022

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Mathematics of Computation

  • ISSN

    0025-5718

  • e-ISSN

    1088-6842

  • Volume of the periodical

    91

  • Issue of the periodical within the volume

    337

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    11

  • Pages from-to

    2335-2345

  • UT code for WoS article

    000802279400001

  • EID of the result in the Scopus database

    2-s2.0-85134403942