An expression for Riemann Siegel function

There are many analytic functions U (t) satisfying Z (t) =2\ e^{i (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 (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.