Serre's famous paper Analogues K"ahl'eriens de Certaines Conjectures de Weil proves an analogue of the Weil conjectures for compact K"ahler manifolds. It would go on to inspire the line of attack that eventually solved the Weil conjectures.

I would like to know is whether the result had any applications or consequences in complex geometry. Since I guess this is a a little broad of a question for this site, let me write: Can anyone name a substantial result in complex geometry that uses Serre's zeta function in a non-trivial way. (Apologies for fluffy words like substantial and non-trivial.)

Serre's famous paper Analogues Kählériens de Certaines Conjectures de Weil proves an analogue of the Weil conjectures for compact Kähler manifolds. It would go on to inspire the line of attack that eventually solved the Weil conjectures.

I would like to know is whether the result had any applications or consequences in complex geometry. Since I guess this is a little broad of a question for this site, let me write: Can anyone name a substantial result in complex geometry that uses Serre's zeta function in a non-trivial way. (Apologies for fluffy words like substantial and non-trivial.)