Let L/K be a finite Galois extension of complete discrete valuation fields whose fields are finite and of characteristics p $>$ 0. Let v$_k$ be the normalized valuation on K, and v$_L$ the normalization of the unique extension w of v$_k$ to L. G is the Galois group of this extension.
Define $\phi_{L/K}$ : [$-$1, $\infty$) $\rightarrow$ [$-$1, $\infty$) as follows. For s $\geq$ 0, let $\phi_{L/K}$(s) = $\int_{0}^{s}$ $\frac{dx}{(G_0 : G_x)}$, for s $<$ 0, let $\phi_{L/K}$(s) = s. And $\psi_{L/K}$ is the inverse of $\phi_{L/K}$
Assume L/K is a cyclic extension of degree p which is totally ramified. Describe the lower ramification subgroups G$_i$. And compute $\psi_{L/K}$.