, Volume 106, Issue 1, pp 57-63

Primitive lattice points in rational ellipses and related arithmetic functions

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Assuming the Riemann Hypothesis to be true, an asymptotic with a sharp error term is established for the number of primitive lattice points inside a rational ellipseau 2+buv+cv 2x (a, b, c integers,b 2−4ac<0). A generalization of the result is given applying (as an example) to counting functions of Pythagorean triangles.