TY - JOUR
ID - 1169
TI - Spatial statistics for lattice points on the sphere I: Individual results
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Bourgain, J.
AU - Rudnick, Z.
AU - Sarnak, P.
AD -
Y1 - 2017
PY - 2017
VL - 43
IS - Issue 4 (Special Issue)
SP - 361
EP - 386
KW - Sums of three squares
KW - spatial statistics
KW - Ripley's functions
DO -
N2 - We study the spatial distribution of point sets on the sphere obtained from the representation of a large integer as a sum of three integer squares. We examine several statistics of these point sets, such as the electrostatic potential, Ripley's function, the variance of the number of points in random spherical caps, and the covering radius. Some of the results are conditional on the Generalized Riemann Hypothesis.
UR - http://bims.iranjournals.ir/article_1169.html
L1 - http://bims.iranjournals.ir/article_1169_fba25bf5c43b78fe1eb1c4b9a4835c11.pdf
ER -