The Vriational Version of Riemann Hypothesis

In this paper, We suggest a new formulation of the Riemann Hypothesis as a variational problem in an appropriately defined function space F by associating each element f∈F with a functional ε(f) (we call it energy functional), such that ε(f)=0 if and only if the real parts of the zeros of the function f equal (1/2). In this framework, we prove that Riemann Hypothesis is true if and only if there exist a fllow f_{t}, starting from an arbitray funtion f₀∈F, such that each f_{t}∈F, lim_{t→∞}(f_{t})=f_{∞} is an element of F, and ε(f_{∞})=0