Primitive lattice points inside an ellipse
| dc.creator | Nowak, Werner Georg | |
| dc.date | 2003-07-21 | |
| dc.date.accessioned | 2026-07-07T06:26:52Z | |
| dc.date.available | 2026-07-07T06:26:52Z | |
| dc.description | Let Q(u,v) be a positive definite binary quadratic form with arbitrary real coefficients. For large real x, one may ask for the number B(x) of primitive lattice points (integer points (m,n) with gcd(m,n) = 1) in the ellipse disc Q(u,v) < x, in particular, for the remainder term R(x) in the asymptotics for B(x). While upper bounds for R(x) depend on zero-free regions of the zeta-function, and thus, in most published results, on the Riemann Hypothesis, the present paper deals with a lower estimate. It is proved that the absolute value of R(x) is, in integral mean, at least a positive constant c times x^{1/4}. Furthermore, it is shown how to find an explicit value for c, for each specific given form Q. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0307279 | |
| dc.identifier | http://arxiv.org/abs/math/0307279 | |
| dc.identifier | Czechosl. Math. J. 55 (2005), 187-206 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/97243 | |
| dc.subject | Number Theory | |
| dc.subject | 11P21 | |
| dc.title | Primitive lattice points inside an ellipse | |
| dc.type | text |