ANALYTIC PROPERTIES OF DIRICHLET SERIES OBTAINED FROM THE ERROR TERM IN THE DIRICHLET DIVISOR PROBLEM

作者：Furuya Jun^*; Tanigawa Yoshio

来源：Pacific Journal of Mathematics, 2010, 245(2): 239-254.

• analytic continuation
• Dirichlet series
• divisor problem
• double zeta function
• orders of Dirichlet series

We discuss some analytic properties of Dirichlet series
Y (s) = Sigma(infinity)(n=1) d(n)Delta(n)n(-s) for Re s > 5/4,
where d (n) is the divisor function and Delta(x) is the error term in the Dirichlet divisor problem. In particular, we study an analytic continuation and an order of Y (s). As applications, we study an analytic continuation and orders of several kinds of Dirichlet series related to Delta(x).

• 出版日期2010-4