The Weighted Mean Value Of Hurwitz Zeta Function And Periodic Zeta Function

Hurwitz zeta function and Periodic zeta function plays a very important role in analytic number theory,many scholars have made extensive and in-depth studies on the mean value and hybird mean value of Hurwitz zeta function or Periodic zeta function,this paper will discuss the weighted mean value of Hurwitz zeta function and Periodic zeta function on the basis of predecessors' research Using the elemental methods and analytic method,based on the previous mode of valuation,this article will study the hybird mean value of Hurwitz zeta function with generalized Cochrane sum or generalized Kloosterman sum and the hybird mean value of Periodic zeta function with Cochrane sum or Dedekind sum.The specific contents are as follows1.According to the definition and properties of generalized Cochrane sum,we study the hybird mean value of Hurwitz zeta function?Kloosterman sum and generalized Cochrane sum,and get the asymptotic formula as follows2.Studying the hybird mean value of Hurwitz zeta function?generalized Kloosterman sum and Cochrane sum or generalized Cochrane sum,we use ana-lytic method to calculate the asymptotic formula as follows and3.Discussing the hybird mean value of Periodic zeta function and Cochrane sum or Dedekind sum,we get the asymptotic formula for and...