Isao Kiuchi

Bounds for triple zeta-functions

Abstract In the present paper we consider the problem of the order of magnitude for the triple zeta-functions of Euler-Zagier type in the region 0≤ ℜ sj j = 1,2,3). We apply the Euler-Maclaurin summation formula and van der Corputs method of multiple exponential sums to the triple zeta-functions.

On Sums of Weighted Averages of gcd-Sum Functions

Let

Bounds for double zeta-functions

\gcd(j,k)

Sums of averages of gcd-sum functions

be the greatest common divisor of the integers

The mean value theorem of the divisor problem for short intervals

j

ON ARITHMETICAL FUNCTIONS RELATED TO THE RAMANUJAN SUM

and

The mean value formula for the approximate functional equation of ζ2(s) in the critical strip II

k

Sums of averages of generalized Ramanujan sums

. In this paper, we give several interesting asymptotic formulas for weighted averages of the

Analytic properties of double zeta-functions

\gcd

Sums of products of generalized Ramanujan sums

-sum function