Mittlere Darstellungen natürlicher Zahlen als Differenz zweier k-ter Potenzen

Lattice points in multidimensional bodies

“…Sarnak (1997) and Wanderkam (1999) consider forms of degree 2 and 4 respectively. For su½ciently large dimensions and p b 2, the bound of Theorem 1.3 improves a result Or dÀ2dad1 s log r s , for d p À 1 and even p, of Randol (1966) Kra Ètzel (1973) extended this result to the case of odd p and functions Qx jx 1 j p Á Á Á jx d j p . They noticed as well that in low dimensions d`p À 1 bounds as in Theorem 1.3 do not hold.…”

On sums and differences of two relative prime cubes

“…For the estimate was improved recently to the accuracy stated here by KUBA [9], in the context of a more general problem involving congruence conditions. For Rj¡(u), KRÄTZEL'S result [6] was refined by MÜLLER and the author [12] up to the order term 0(u ánF +e ). Thus we start here from formula (5) of that paper, viz.…”

“…Asymptotic results of this type were established first by KRÄTZEL [5], [6], who obtained the somewhat less precise order term 0(u*t~e°), with unspecified 6q > 0. (See also the exposition in KRÄTZEL'S textbook [8].)…”

The local contribution of zeros of curvature to lattice point asymptotics

“…H is periodic and given by some absolutely convergent Fourier series which vanishes if and only if P is a point of inflection whose tangent contains the origin (Randol [11] and Krätzel [3] proved this for the special case where K is a Lamé curve).…”