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
An analytic function f in the unit disk D ：= {z ∈ C ： ｜z｜ 〈 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k（z） ：= z/（1-z）2, z ∈ D, if there exists δ ∈ （-π/2,...An analytic function f in the unit disk D ：= {z ∈ C ： ｜z｜ 〈 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k（z） ：= z/（1-z）2, z ∈ D, if there exists δ ∈ （-π/2,π/2） such that Re {eiδ（1-z）2f′（z）} 〉 0, z ∈ D. For the class C（k） of all close-to-convex functions with respect to k, related to the class of functions convex in the positive direction of the imaginary axis, the Fekete-Szego problem is studied.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.
文摘An analytic function f in the unit disk D ：= {z ∈ C ： ｜z｜ 〈 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k（z） ：= z/（1-z）2, z ∈ D, if there exists δ ∈ （-π/2,π/2） such that Re {eiδ（1-z）2f′（z）} 〉 0, z ∈ D. For the class C（k） of all close-to-convex functions with respect to k, related to the class of functions convex in the positive direction of the imaginary axis, the Fekete-Szego problem is studied.
