Abstract
As a generalization of the sphere problem (cf. VINOGRADOV [7]) the present paper deals with estimates for the number of lattice points (points of the space with integral coordinates) in regions defined by xa+ya+za≦Ra, x≧0, y≧0, z≧0. In particuliar, the case 0<a≦1/3 is considered (the case a>2 has been treated by KRÄTZEL [2]), and it appears that the exact asymptotic behaviour of the remainder term can be determined. Furthermore an asymptotic expansion of the remainder term is established containing the more valid terms the smaller the exponent a is.
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Nowak, W.G. Ein dreidimensionales Gitterpunktproblem. Manuscripta Math 33, 63–80 (1980). https://doi.org/10.1007/BF01298339
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DOI: https://doi.org/10.1007/BF01298339