What do these rests mean? Carcassi Etude no. 1 op. 60 (Guitar)

Question

The quarter note rest and the half note rest in the first measure. I listened to the piece and they play the d and g note the rest is under.

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It is just pointing out that nothing is playing in the bass notes?

Answer 1

That's correct: the rests show that the bass "voice" is resting while the upper "voice" continues.

The double stem on the first note of each measure is also an indication that there are two voices — in those cases both are "singing" (playing) the same note simultaneously.

See also Rest above a note in a piano piece and the questions linked and related to it.

Answer 2

It's exactly that - think of the notes with upstems being played using fingers, and those with downstems played with thumb.

There are two distinct, but joined parts here - the 'tune' and the 'accompaniment'. tune with upstems, accompaniment with downstems. In reality the 1st note could be played using either finger or thumb, (not both!) and strictly speaking ought to have a quaver rest in the top half. And actually sounds better using thumb. But that lower note needs to last for one beat, not half, so gets written as such (the accompaniment is often a note which could last for the whole bar, but not here).

EDIT: I've voted to re-open, as the other question, while it contains similar answers, shows the rest as something not being played, BUT there are other notes being played instead. In this, it specifically shows that the lower note only lasts for that one beat - hence the ensuing rests. Picky, yes, but I feel, an important difference.