Geodesic
Bounds and behaviour of the quantities $P(x)$, $\Delta(x)$ on short intervals
Izvestiya. Mathematics , Tome 80 (2016) no. 6, pp. 1213-1230

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the dependence of upper bounds for the quantity $|P(n)|$ on certain properties of the behaviour of $|P(x)|$ in a neighbourhood of the point $x=n$. In particular, it is proved that, if $n$ is a point of local maximum of the quantity $|P(x)|$, where $|P(n)|>Cn^{1/4}$ and the maximum is broad ($|P(x)-P(n)|$, $B1$, if $|x-n|$), then $|P(n)|>Cn^{1/4+\varepsilon}$.
Keywords: circle problem and divisor problem, Voronoi–Hardy and Landau formulae, short intervals. 
@article{IM2_2016_80_6_a10,
     author = {D. A. Popov},
     title = {Bounds and behaviour of the quantities $P(x)$, $\Delta(x)$ on short intervals},
     journal = {Izvestiya. Mathematics },
     pages = {1213--1230},
     publisher = {mathdoc},
     volume = {80},
     number = {6},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2016_80_6_a10/}
}
TY  - JOUR
AU  - D. A. Popov
TI  - Bounds and behaviour of the quantities $P(x)$, $\Delta(x)$ on short intervals
JO  - Izvestiya. Mathematics 
PY  - 2016
SP  - 1213
EP  - 1230
VL  - 80
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2016_80_6_a10/
LA  - en
ID  - IM2_2016_80_6_a10
ER  - 
%0 Journal Article
%A D. A. Popov
%T Bounds and behaviour of the quantities $P(x)$, $\Delta(x)$ on short intervals
%J Izvestiya. Mathematics 
%D 2016
%P 1213-1230
%V 80
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2016_80_6_a10/
%G en
%F IM2_2016_80_6_a10
D. A. Popov. Bounds and behaviour of the quantities $P(x)$, $\Delta(x)$ on short intervals. Izvestiya. Mathematics , Tome 80 (2016) no. 6, pp. 1213-1230. http://geodesic.mathdoc.fr/item/IM2_2016_80_6_a10/