The notation in the piano part is just a possible way to voice a C7(b9) chord. It’s not uncommon in a jazz setting for chordal instruments (i.e. piano, guitar, vibes) to omit the root or even the fifth (especially if it’s a natural fifth or there’s a b13 in the chord) entirely in chord voicings, particularly when chords have a lot of extensions. Roots and fifths aren’t particularly colorful, so as long as someone (read: the bassist) is sticking to them for the most part that frees up whoever’s comping to play more interesting voicings. This is very different from various pop genres, folk traditions, musical theater, and even the continuo in baroque music where chordal instruments are often playing the roots in their chord voicings.uhm, so it's G Db E Bb (it should be b somewhere on the clef) marked as C7b9?
this notation does make some sense and it's a nice chord of three tritones, thanks for such a nice example! I'd write it as Gdim tho.
In big band horn arrangements, unless there’s a root in the melody, it’s common to avoid roots in all of the voices except for bass trombone and/or bari sax.