An expression for Riemann Siegel function

There are many analytic functions $U(t)$ satisfying Z(t)=2\ eiϑ(t)U(t)\. Here, we consider an entire function L(s) such that U(t)= L(12+it) is one of the simplest among them. We obtain an expression for the Riemann-Siegel function $Z(t)$ in terms of the zeros of L(s). Implicitly, the function L(s) is considered by Riemann in his paper on Number Theory. Riemann spoke of having used an expression for Ξ(t) in his demonstration that most of the non-trivial zeros of the zeta function lie on the critical line. Therefore, any expression deserves a study.