Riemann Products II

The consideration of ordinals $N = p_1 p_2 p_3 \cdots p_k$, where all prime factors $p_i$ are distinct, occurs as the Pauli exclusion principle for the Riemann gas, whose partition function is the Riemann zeta function.

The product expression for the inverse zeta function is always well defined for finite products, which define a sequence of functions $\zeta_N$ for $N$ such a Pauli ordinal. Showing that the limit $N \rightarrow \infty$ leads to a well defined zeta function for basically all $s$ values is equivalent to the Riemann hypothesis.