TITLE: Less fundamental applications of Zeta regularization:
QUESTION [6 upvotes]: As we all know, zeta regularization is used in Quantum field theory and calculations regarding the Casimir effect.

Are there less fundamental applications of zeta function regularization? By "less fundamental" I mean 
  it 'naturally' pops up in more of an artificially / purely mathematically ideal constructed scenario.

Thanks!

REPLY [5 votes]: Zeta function regularization computes the asymptotics of smoothed sums. 
https://terrytao.wordpress.com/2010/04/10/the-euler-maclaurin-formula-bernoulli-numbers-the-zeta-function-and-real-variable-analytic-continuation/
Also, the regularized determinant of the Laplacian is related to the Ray-Singer analytic torsion, which is equal to the Reidemeister torsion:
https://en.wikipedia.org/wiki/Analytic_torsion