Geodesic
Distances from points to planes
P. Birklbauer1 ; A. Iosevich1 ; T. Pham2
1 Department of Mathematics University of Rochester Rochester, NY 14627, U.S.A.
2 Department of Mathematics University of California, San Diego La Jolla, CA 92093, U.S.A.
Acta Arithmetica, Tome 186 (2018) no. 3, pp. 219-224

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We prove that if $E \subset {\Bbb F}_q^d$, $d \ge 2$, and $F \subset \operatorname{Graff}(d-1,d)$, the set of affine $d-1$-dimensional planes in ${\Bbb F}_q^d$, then $|\Delta(E,F)| \ge {q}/{2}$ if $|E|\,|F| \gt q^{d+1}$, where $\Delta(E,F)$ is the set of distances from points in $E$ to planes in $F$. In dimension three and higher this significantly improves the exponent obtained by Pham, Phuong, Sang, Valculescu and Vinh (2018), who obtain the same conclusion under the assumption $|E|\,|F| \ge Cq^{{4d}/{3}}$.
DOI : 10.4064/aa171110-23-8
Keywords: prove subset bbb subset operatorname graff d set affine d dimensional planes bbb delta where delta set distances points planes dimension three higher significantly improves exponent obtained pham phuong sang valculescu vinh who obtain conclusion under assumption

P. Birklbauer 1 ; A. Iosevich 1 ; T. Pham 2

1 Department of Mathematics University of Rochester Rochester, NY 14627, U.S.A.
2 Department of Mathematics University of California, San Diego La Jolla, CA 92093, U.S.A. 
@article{10_4064_aa171110_23_8,
     author = {P. Birklbauer and A. Iosevich and T. Pham},
     title = {Distances from points to planes},
     journal = {Acta Arithmetica},
     pages = {219--224},
     publisher = {mathdoc},
     volume = {186},
     number = {3},
     year = {2018},
     doi = {10.4064/aa171110-23-8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa171110-23-8/}
}
TY  - JOUR
AU  - P. Birklbauer
AU  - A. Iosevich
AU  - T. Pham
TI  - Distances from points to planes
JO  - Acta Arithmetica
PY  - 2018
SP  - 219
EP  - 224
VL  - 186
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa171110-23-8/
DO  - 10.4064/aa171110-23-8
LA  - en
ID  - 10_4064_aa171110_23_8
ER  - 
%0 Journal Article
%A P. Birklbauer
%A A. Iosevich
%A T. Pham
%T Distances from points to planes
%J Acta Arithmetica
%D 2018
%P 219-224
%V 186
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/aa171110-23-8/
%R 10.4064/aa171110-23-8
%G en
%F 10_4064_aa171110_23_8
P. Birklbauer; A. Iosevich; T. Pham. Distances from points to planes. Acta Arithmetica, Tome 186 (2018) no. 3, pp. 219-224. doi: 10.4064/aa171110-23-8

Cité par Sources :