Local zeta function: Difference between revisions

Revision as of 02:01, 9 December 2020

Revision as of 02:04, 9 December 2020

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:<math>G(t) = N_1t +N_2t^2/2 + N_3t^3/3 +\cdots \,</math>.

The correct definition for ''Z''(''t'') is to makeset log ''Z'' equal to ''G'', and so

:<math>Z= \exp (G(t)) \, </math>

we will haveand ''Z''(0) = 1, since ''G''(0) = 0, and ''Z''(''t'') is ''a priori'' a [[formal power series]].

Note that theThe [[logarithmic derivative]]

:<math>Z'(t)/Z(t) \,</math>