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It is known that not all summation methods are linear and stable. Zeta function regularization is in general nonlinear. However, in some cases formal manipulations with zeta function regularization (assuming linearity of sums) lead to correct results. We consider several examples and show why this happens.
Nikolaos Stergiopulos, Georgios Rovas, Vasiliki Bikia
Romain Christophe Rémy Fleury, Benjamin Apffel