Extreme values for Sn(σ,t) near the critical line
Journal article, Peer reviewed
Accepted version
![Thumbnail](/ntnu-xmlui/bitstream/handle/11250/2640718/Extreme%2bvalues%2bfor%2bSn%2528sigma%252Ct%2529%2bnear%2bthe%2bcritical%2bline.pdf.jpg?sequence=6&isAllowed=y)
Åpne
Permanent lenke
http://hdl.handle.net/11250/2640718Utgivelsesdato
2019Metadata
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- Institutt for matematiske fag [2450]
- Publikasjoner fra CRIStin - NTNU [38069]
Originalversjon
10.1016/j.jnt.2018.12.009Sammendrag
Let S(σ, t) =1πargζ(σ+it)be the argument of the Riemann zeta function at the point σ+itof the critical strip. Fo r n ≥1and t >0we defineSn(σ, t)=t∫0Sn−1(σ, τ)dτ+δn,σ,where δn,σis a specific constant depending on σand n. Let 0 ≤β<1be a fixed real number. Assuming the Riemann hypothesis, we show lower bounds for the maximum of the function Sn(σ, t)on the interval Tβ≤t ≤Tand near to the critical line, when n ≡1mod4. Similar estimates are obtained for |Sn(σ, t)|when n ≡1mod4. This extends the results of Bondarenko and Seip [7]for a region near the critical line. In particular we obtain some omega results for these functions on the critical line.