What is Motivic L-function?, Explain Motivic L-function, Define Motivic L-function

#MotivicL-function #audioversity
~~~ Motivic L-function ~~~

Title: What is Motivic L-function?, Explain Motivic L-function, Define Motivic L-function
Created on: 2019-01-22

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Description: In mathematics, motivic L-functions are a generalization of Hasse–Weil L-functions to general motives over global fields. The local L-factor at a finite place v is similarly given by the characteristic polynomial of a Frobenius element at v acting on the v-inertial invariants of the v-adic realization of the motive. For infinite places, Jean-Pierre Serre gave a recipe in for the so-called Gamma factors in terms of the Hodge realization of the motive. It is conjectured that, like other L-functions, that each motivic L-function can be analytically continued to a meromorphic function on the entire complex plane and satisfies a functional equation relating the L-function L of a motive M to L, where M∨ is the dual of the motive M.

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