Hugh L Montgomery - On a question of Ramachandra

hrj:95 - Hardy-Ramanujan Journal, January 1, 1982, Volume 5 - 1982 - https://doi.org/10.46298/hrj.1982.95
On a question of RamachandraArticle

Authors: hugh L Montgomery

    For each positive integer k, let ak(n)=(pps)k=n=1ak(n)ns,

    where σ=Re(s)>1, and the sum on the left runs over all primes p. This paper is devoted to proving the following theorem: If 1/2<σ<1, then maxk(nNak(n)2n2σ)1/2k(logN)1σ/loglogN
    and (n=1ak(n)2n2σ)1/2kk1σ/(logk)σ.
    The constants implied by the sign may depend upon σ. This theorem has applications to the Riemann zeta function.


    Volume: Volume 5 - 1982
    Published on: January 1, 1982
    Imported on: March 3, 2015
    Keywords: [MATH]Mathematics [math]

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