RLC filter as amplifier?
It can amplify the voltage (near to the resonant frequency) at the expense of load current. In other words you can't get power amplification. The frequency response will look like this: -



For a high damping (R is low in value, zeta = 0.5) the frequency response will be the lower blue curve but, with a high value resistor several tens of dB voltage amplification can occur. That amplification is not constant with frequency (as you can see) but can be significant from half resonance to a little over resonance.

A problem of significance occurs if you try and get too much amplification. Consider the situation when damping is really low i.e. resistance really high. For now the resistor can be ignored and what you are left with is a series resonant LC tuned circuit to ground. As you may know, a series resonant circuit (with zero or very low damping) will act as a short circuit - if you try and apply a voltage input at the resonant frequency it will be shorted by the LC. Because the inductor will never be perfect the input impedance won't be zero but the DC resistance of the inductor (maybe an ohm).