On the representation of integers as a sum of mixed powers
The author uses the Hardy-Littlewood method to establish an asymptotic formula for the number of representations of a large number in the form \(n^2_1+ n^3_2+ n^3_3+ n^3_4+ n^3_5+ n^6_6+ n^8_7\). This extends results of \textit{M. Lu} [Acta Arith. 58, 89-102 (1991; Zbl 0725.11050)], in whose work at least one of \(n_6\), \(n_7\) appeared to a lower degree. The formula assumes the shape \(c\sigma (n) n^{73/72}+ O(n^{73/ 72-\delta})\), where \(\delta>0\) and \(\sigma (n)\) denotes a ``singular series''. (The exponent \(\delta\) is however typeset as \(\sigma\)).
scientific article; zbMATH DE number 846496