In 1927, Polya proved that the Riemann hypothesis is equivalent to the hyperbolicity of Jensen polynomials for the Riemann zeta function ζ(s) at its point of symmetry. This hyperbolicity has been proved for degrees d ≤3. We obtain an asymptotic formula for the central derivatives ζ(2n)(1/2) that is accurate to all orders, which allows us to prove the hyperbolicity of all but finitely many of the Jensen polynomials of each degree. Moreover, we establish hyperbolicity for all d ≤8. These results follow from a general theorem which models such polynomials by Hermite polynomials. In the case of the Riemann zeta function, this proves the Gaussian unitary ensemble random matrix model prediction in derivative aspect. The general theorem also allows us to prove a conjecture of Chen, Jia, and Wang on the partition function.

New relations for the Riemann zeta function (RZF) by defining supplementary partial product functions are developed in this paper. Relations are based on partial products of prime numbers with recourse
to product form of the RZF found by unique factorization in Z. This paper is in pursuit of generating new identities involving RZF including summations, products, and limits mostly in the matter of
multiplicative property of Euler products and by applying Taylor series. This is done with the intention
of relating some classical and newly defined functions (using multiplicative Jordanís totient function and
primorial sequence) to RZF in the form of theorems and proofs.