Zeta-function regularization of infinite series is the most commonly used in QFT applications. However, occasionally other schemes are employed which, allegedly, suit the nature (most noticeably the underlying symmetries) of the problem at hand. An alternative to the zeta-function (used for instance at the bottom of Page 6 in hep-th/0311021) is to sum all the terms "on equal footing", where the quoted phrase refers to the fact that some other methods employ regulators (e.g. $e^{-m\epsilon}$ for the $m$'th term) to exponentially (or otherwise) suppress the consequitive terms, and then throw away the infinities that turn up while removing the regulator by taking limits. This alternative, on the other hand, just sums the series up to some cutoff $N$ and then removes the $N$-dependent parts. For example, the sum of integers would be zero with this regularization, as $N(N+1)/2$ has no $N$-independent part.
I would appreciate it if someone can elaborate on the issue, by explaining why this alternative regularization scheme respects supersymmetry (as claimed in the provided reference) but the zeta-function regularization does not.
