Let B<sub>α</sub>（α）be an additive function on a ring of integers in the quadratic number field Q（（1/2）d）given by B<sub>α</sub>（α）=∑<sub>p丨α</sub><sup>*</sup...Let B<sub>α</sub>（α）be an additive function on a ring of integers in the quadratic number field Q（（1/2）d）given by B<sub>α</sub>（α）=∑<sub>p丨α</sub><sup>*</sup>N<sup>α</sup>（p）with a fixed α】0,where the asterisk means that the summation is over the non-associate prime divisors p of an integer α in Q（（1/2）d）,N（α）is the norm of α.In this paper we obtain the asymptotic formula of ∑<sub>N</sub>（α）≤<sub>x</sub> <sup>*</sup>B<sub>α</sub>（α）in the case where the class-number of Q（（1/2）d）is one.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘Let B<sub>α</sub>（α）be an additive function on a ring of integers in the quadratic number field Q（（1/2）d）given by B<sub>α</sub>（α）=∑<sub>p丨α</sub><sup>*</sup>N<sup>α</sup>（p）with a fixed α】0,where the asterisk means that the summation is over the non-associate prime divisors p of an integer α in Q（（1/2）d）,N（α）is the norm of α.In this paper we obtain the asymptotic formula of ∑<sub>N</sub>（α）≤<sub>x</sub> <sup>*</sup>B<sub>α</sub>（α）in the case where the class-number of Q（（1/2）d）is one.
