Well, we can use Mathematics to compute what happens.
We write, for the input voltage:
$$\text{V}_\text{in}\left(t\right)=\hat{\text{v}}_\text{in}\cdot\sin\left(\omega t+\varphi\right)=\hat{\text{v}}_\text{in}\cdot\cos\left(\omega t+\varphi+\frac{\pi}{2}\right)\tag1$$
So, the complex input voltage is given by:
$$\underline{\text{V}}_{\space\text{in}}=\hat{\text{v}}_\text{in}\cdot\exp\left(\left(\varphi+\frac{\pi}{2}\right)\text{j}\right)\tag2$$
Now, the complex input impedance is given by:
$$\underline{\text{Z}}_{\space\text{in}}=\text{R}+\text{j}\omega\text{L}||\frac{1}{\text{j}\omega\text{C}}=\text{R}+\frac{\text{j}\omega\text{L}\cdot\frac{1}{\text{j}\omega\text{C}}}{\text{j}\omega\text{L}+\frac{1}{\text{j}\omega\text{C}}}=\text{R}+\frac{\text{L}}{\text{C}}\cdot\frac{1}{\frac{1}{\omega\text{C}}-\omega\text{L}}\cdot\text{j}\tag3$$
The complex input current is given by:
$$\underline{\text{I}}_{\space\text{in}}=\frac{\underline{\text{V}}_{\space\text{in}}}{\underline{\text{Z}}_{\space\text{in}}}=\frac{\hat{\text{v}}_\text{in}\cdot\exp\left(\left(\varphi+\frac{\pi}{2}\right)\text{j}\right)}{\text{R}+\frac{\text{L}}{\text{C}}\cdot\frac{1}{\frac{1}{\omega\text{C}}-\omega\text{L}}\cdot\text{j}}\tag4$$
The time function for the input current is given by:
$$\space\text{I}_\text{in}\left(t\right)=\left|\frac{\underline{\text{V}}_{\space\text{in}}}{\underline{\text{Z}}_{\space\text{in}}}\right|\cdot\cos\left(\omega t+\arg\left(\frac{\underline{\text{V}}_{\space\text{in}}}{\underline{\text{Z}}_{\space\text{in}}}\right)\right)=$$
$$\frac{\left|\underline{\text{V}}_{\space\text{in}}\right|}{\left|\underline{\text{Z}}_{\space\text{in}}\right|}\cdot\cos\left(\omega t+\arg\left(\underline{\text{V}}_{\space\text{in}}\right)-\arg\left(\underline{\text{Z}}_{\space\text{in}}\right)\right)\tag5$$
The complex voltage across the parallel part is given by:
$$\underline{\text{V}}_{\space\text{p}}=\underline{\text{Z}}_{\space\text{p}}\cdot\underline{\text{I}}_{\space\text{p}}=\underline{\text{Z}}_{\space\text{p}}\cdot\underline{\text{I}}_{\space\text{in}}=\frac{\text{L}}{\text{C}}\cdot\frac{1}{\frac{1}{\omega\text{C}}-\omega\text{L}}\cdot\text{j}\cdot\frac{\hat{\text{v}}_\text{in}\cdot\exp\left(\left(\varphi+\frac{\pi}{2}\right)\text{j}\right)}{\text{R}+\frac{\text{L}}{\text{C}}\cdot\frac{1}{\frac{1}{\omega\text{C}}-\omega\text{L}}\cdot\text{j}}=$$
$$\frac{\text{L}}{\text{C}}\cdot\frac{\hat{\text{v}}_\text{in}\cdot\exp\left(\left(\varphi+\frac{\pi}{2}\right)\text{j}\right)}{\text{R}\left(\frac{1}{\omega\text{C}}-\omega\text{L}\right)+\frac{\text{L}}{\text{C}}\cdot\text{j}}\cdot\text{j}\tag6$$
At resonance we know that:
$$\frac{1}{\omega\text{C}}-\omega\text{L}=0\tag7$$
So:
$$\underline{\text{V}}_{\space\text{p}}=\frac{\text{L}}{\text{C}}\cdot\frac{\hat{\text{v}}_\text{in}\cdot\exp\left(\left(\varphi+\frac{\pi}{2}\right)\text{j}\right)}{0+\frac{\text{L}}{\text{C}}\cdot\text{j}}\cdot\text{j}=\hat{\text{v}}_\text{in}\cdot\exp\left(\left(\varphi+\frac{\pi}{2}\right)\text{j}\right)\tag8$$
Concluding:
$$\underline{\text{V}}_{\space\text{p}}=\underline{\text{V}}_{\space\text{in}}\tag9$$