Convolution of Riemann zeta-values

Dedicated to Professor Isao Wakabayashi with great respect

抄録

In this note we are going to generalize Prudnikov's method of using a double integral to deduce relations between the Riemann zeta-values, so as to prove intriguing relations between double zeta-values of depth 2. Prior to this, we shall deduce the most well-known relation that expresses the sum ∑_{j=1}^m-2 ξ(j+1)ξ(m-j) in terms of ξ_2(1, m).