Let Q(x) be the number of square-full numbers not exceeding x, x is a suffciently large positive number. Assuming the Riemann hypothesis to be tenable, an asymptotic formula of Q(x) with a new error is obtained.
Let △（x）be the error term in the asymptotic formula for the counting function of square-full integers.In the present paper it is proved that △（x）=O(x<sup>27/4+ε</sup>),which improves on the exponent...Let △（x）be the error term in the asymptotic formula for the counting function of square-full integers.In the present paper it is proved that △（x）=O(x<sup>27/4+ε</sup>),which improves on the exponent 33/5 obtained by X.D.CAO.展开更多
文摘Let Q(x) be the number of square-full numbers not exceeding x, x is a suffciently large positive number. Assuming the Riemann hypothesis to be tenable, an asymptotic formula of Q(x) with a new error is obtained.
基金Project supported by the National Natural Science Foundation of China
文摘Let △（x）be the error term in the asymptotic formula for the counting function of square-full integers.In the present paper it is proved that △（x）=O(x<sup>27/4+ε</sup>),which improves on the exponent 33/5 obtained by X.D.CAO.
