Vol. 245, No. 2, 2010

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Analytic properties of Dirichlet series obtained from the error term in the Dirichlet divisor problem

Jun Furuya and Yoshio Tanigawa

Vol. 245 (2010), No. 2, 239–254

We discuss some analytic properties of Dirichlet series Y (s) = n=1d(n)Δ(n)ns for Re s > 54, where d(n) is the divisor function and Δ(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 Δ(x).

analytic continuation, Dirichlet series, divisor problem, double zeta function, orders of Dirichlet series
Mathematical Subject Classification 2000
Primary: 11L07, 11M41
Received: 1 April 2009
Revised: 14 September 2009
Accepted: 4 January 2010
Published: 1 April 2010
Jun Furuya
Department of Integrated Arts and Science
Okinawa National College of Technology
Nago, Okinawa, 905-2192
Yoshio Tanigawa
Graduate School of Mathematics
Nagoya University
Nagoya, 464-8602