Abstract
Lagarias, Montgomery, and Odlyzko proved that there exists an effectively computable absolute constant A 1 such that for every finite extension K of ℚ, every finite Galois extension L of K with Galois group G and every conjugacy class C of G, there exists a prime ideal 𝔭 of K which is unramified in L, for which L/K 𝔭=C, for which N K/ℚ 𝔭 is a rational prime, and which satisfies N K/ℚ 𝔭≤2d L A 1 . In this paper we show without any restriction that N K/ℚ 𝔭≤d L 12577 if L≠ℚ, using the approach developed by Lagarias, Montgomery, and Odlyzko.
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