On the zeros of Dirichlet Eta Function

We consider the analytic continuation of Riemann's Zeta Function derived from Dirichlet Eta Function $\eta(s)$ which is evaluated at $s = \frac{1}{2} + \sigma + i \omega$, where $\sigma, \omega$ are real and compute inverse Fourier transform of $\Gamma(\frac{s}{2}) \eta(s)$ and derive $E_p(t)$. We study the properties of $E_p(t)$ and a promising new method is presented which could be used to show that the Fourier Transform of $E_p(t)$ given by $E_{p\omega}(\omega) = \xi(\frac{1}{2} + \sigma + i \omega)$ does not have zeros for finite and real $\omega$ when $0 < |\sigma| < \frac{1}{2}$, corresponding to the critical strip excluding the critical line.