A variant of the Barban-Davenport-Halberstam Theorem

Details A variant of the Barban-Davenport-Halberstam Theorem A variant of the Barban-Davenport-Halberstam Theorem

2012-01-29

arxiv.org/abs/1201.6007v1

International Journal of Number Theory, 7(8):2203-2218, 2011

Mathematics

Number Theory

Scientific paper

10.1142/S179304211100499X

Let $L/K$ be a Galois extension of number fields. The problem of counting the number of prime ideals $\mathfrak p$ of $K$ with fixed Frobenius class in $\mathrm{Gal}(L/K)$ and norm satisfying a congruence condition is considered. We show that the square of the error term arising from the Chebotar\"ev Density Theorem for this problem is small "on average." The result may be viewed as a variation on the classical Barban-Davenport-Halberstam Theorem.

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