关于ζ函数的积分表示

On integral representations for the Zeta-function

主要研究了ζ函数的积分表示形式;通过解析数论的研究方法,利用黎曼ζ函数方程,给出了关于赫尔维茨ζ函数的埃尔米特公式,利用埃尔米特公式得出关于Γ函数的比内第二表达式,通过ζ函数得出Γ函数一些性质.

Integral representations for the Zeta-function was studied,The methods of analytic number theory was used,we shall derive Hermite’s formula for the Hurwitz Zeta-function from the functional equation for the Riemann Zeta-function and derive Binet’s second expression for the gamma function form Hermite’s formula,thus deriving properties of the gamma function from the Zeta-function.