Zeta function regularization: Difference between revisions

Revision as of 15:43, 25 January 2006

Revision as of 16:42, 25 January 2006

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==Relation to other regularizations==

Zeta function regularization gives a nice analytic structure to any sums over an [[arithmetic function]] <math>f(n)</math>. Such sums are known as [[Dirichlet series]]. The regularized form

:<math>\tilde{f}(s) = \sum_{n=1}^\infty f(n)n^{-s}</math>