The double Riemann zeta function (Q2638180)

The Kurokawa tensor product (or the absolute tensor product) of zeta functions means a new zeta function having zeros at sum of zeros of the original zeta functions. The double Riemann zeta function means the Kurokawa tensor product of the Riemann zeta function with itself. It has zeros at sums of any combinations of zeros of the Riemann zeta function, and it is expected to contribute to the proof of the Riemann hypothesis, if we want to prove it in the Deligne's method for congruence zeta functions. The double Riemann zeta function is expressed by an Euler product over all pairs of primes. In this paper, the author obtains the explicit form of the Euler factors of the double Riemann zeta function by duplicating the explicit formula of Deninger. The result gives a refinement of the theorem proved by the reviewer and \textit{N. Kurokawa} [Transl., Ser. 2, Am. Math. Soc. 218, 101--140 (2006) and Tr. St-Petersb. Mat. Obshch. 11, 123--166 (2005; Zbl 1247.11112)], which gave an explicit form of the Euler factors containing an additional parameter \(\alpha\). In this paper the author successfully eliminates the parameter \(\alpha\).