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The \(v\)-function appears in the wild McKay correspondence and it is aninvariant of a Galois extension over a local field which measures about theramification of extension. The ramification filtration is also such invariant.Yasuda presented the problem whether the \(v\)-function is determined byramification filtration. In this paper, we give a formula for the\(v\)-function for 2-dimensional representations of the bicyclic group of order\(p^2\) with \(p\) the characteristic of our base field. Using this formula, weconstruct an example of \(v\)-function not determined by the ramificationfiltration.

The v-function in the wild McKay correspondence is not determined by the ramification filtration