摘要
Let v(n) denote the number of representations of n as the sum of six cubes and twobiquadrates of natural numbers. Then for all sufficiently large n, we have v(n)≥1/(48)~2(log16/15)Γ(4/3)~6Γ(5/4)~2?(Γ(5/2))?(n)n^(3/2),where ?(n) =sum from q=1 to ∞ sum from a=1 (a,q)=1 to q q^(-8)S_3(q,a)~6S_4(q,a)~2c(-an/q) S_k(q,a) =sum from r=1 to q e(ar^k/q).
Let v（n） denote the number of representations of n as the sum of six cubes and twobiquadrates of natural numbers. Then for all sufficiently large n, we have v（n）≥1/（48）<sup>2</sup>（log16/15）Γ（4/3）<sup>6</sup>Γ（5/4）<sup>2</sup>?（Γ（5/2））?（n）n<sup>3/2</sup>,where ?（n） =sum from q=1 to ∞ sum from a=1 （a,q）=1 to q q<sup>-8</sup>S<sub>3</sub>（q,a）<sup>6</sup>S<sub>4</sub>（q,a）<sup>2</sup>c（-an/q） S<sub>k</sub>（q,a） =sum from r=1 to q e（ar<sup>k</sup>/q）.
基金
Project supported by the Alexander von Humboldt-Fund and the National Natutal Science Foundation of China.
