Volume 24 - 2001

1. On some Ramanujan's P-Q Identities

H S Madhusudhan ; M S Mahadeva Naika ; K R Vasuki.
In this paper, we obtain some P-Q eta-function identities of Ramanujan on employing some modular equations in Ramanujan's alternative theory of elliptic functions of signature 4.

2. On the values of the Riemann zeta-function at rational arguments

S Kanemitsu ; Y Tanigawa ; M Yoshimoto.
In a companion paper, ``On multi Hurwitz-zeta function values at rational arguments, Acta Arith. {\bf 107} (2003), 45-67'', we obtained a closed form evaluation of Ramanujan's type of the values of the (multiple) Hurwitz zeta-function at rational arguments (with denominator even and numerator odd), which was in turn a vast generalization of D. Klusch's and M. Katsurada's generalization of Ramanujan's formula. In this paper we shall continue our pursuit, specializing to the Riemann zeta-function, and obtain a closed form evaluation thereof at all rational arguments, with no restriction to the form of the rationals, in the critical strip. This is a complete generalization of the results of the aforementioned two authors. We shall obtain as a byproduct some curious identities among the Riemann zeta-values.