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Adiabatic Invariance (AdI), Hill Equation formalism (HEF), and the LeastAction Principle (LAP), three relevant tools of theoretical physics are hereseparately applied to a one-dimensional parametric oscillator of time-variablefrequency that depends on an integer parameter Lambda. This oscillator issubjected to a perturbation which is a functional of the modulus of RiemannZeta Function (RZF) times an oscillatory function, expecting that nontrivialzeroes could be obtained, in the critical strip, either (i) by optimizing theoscillator AdI, (ii) verifying the Magnus-Winkler equation associated to theoscillator Hill equation, (iii) from evaluating the Action integral of theperturbed oscillator. The optimum value of parameter Lambda is firstly obtainedwhen applying the AdI formalism, and we find that the three formalisms do leadto parametric oscillator states giving the RZF zeroes in arbitrary finiteintervals on the critical line. The parameter Lambda is later replaced by arandom integer-valued function Lambda(sigma) written in terms of twin primes,actually defining an infinite set of perturbed oscillators of differentLagrangian. Nonetheless, when applying the LAP to these oscillators we stillget those Riemann zeroes at the critical line, in spite of both complex planecoordinates varying simultaneously in the critical strip.

Riemann Zeroes from a Parametric Oscillator analyzed with Adiabatic Invariance, Hill Equation and the Least Action Principle