Primitive lattice points in starlike planar sets

On the distribution of primitive Pythagorean triangles

“…Therefore it is natural to search for stronger estimates under the Riemann Hypothesis (RH). The exponent 1/4 in R area (x) was improved by several authors under RH (see [11], [15], [14], [16], [22]). It is also of interest to consider the distributions of P (x), A(x) and H(x) unconditionally in short intervals.…”

“…We shall estimate S 2 in a standard way. The key step is a familiar contour integration technique in the spirit of Montgomery and Vaughan [13], which is used in many occasions when estimating primitive lattice points (for example, see [7], [16], [23]). We only give an outline of the technique here.…”

Simultaneous visibility in the integer lattice

“…Ω-results for E ′ 2 and E ′ 3 have also been obtained [10,47]. (For more details on visible lattice points in planar domains, see [4,5,21,40,46,72,73]. )…”

On the number of primitive Pythagorean triangles

“…The exponent 5/22 can be replaced by 137/604, 127/560, 37/164, 269/1238, as proved respectively by Menzer [4], Müller-Nowak-Menzer [6], Müller and Nowak [5], Nowak [7]. In this paper, we shall prove the following Theorem.…”