BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

An explicit version of Chebotarevâ s density theorem Das, Sourabh


Chebotarevâ s density theorem asserts that the prime ideals are equidistributed over the conjugacy classes of Galois group of any given normal extensions of number fields. An effective version of this theorem was first proved by Lagarias and Odlyzko in 1977. In this talk, I will discuss a new explicit version of Lagarias and Odlyzkoâ s result on Chebotarevâ s density theorem. Some of the main ideas are deriving an explicit formula for the smooth version of a certain prime ideal counting function, and proving new bounds for the number of low-lying zeros for Hecke L-functions to estimate certain sums over the non-trivial zeros of the Dedekind ζ-function. I will give an overview of how these ideas lead to a new explicit version.

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