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Some analogue of Hilbert's irreducibility theorem and the distribution of algebraic number fields

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... for p = 2; also, let λ 1 (2) = 1 and λ n (2) = 1/2 for n ≥ 2. Then a result of Yamamura [26,Proposition 3] states that λ n ( p) is the density of monic polynomials of degree n over Z p having discriminant indivisible by p 2 . Let λ n := p λ n ( p), where the product is over all primes p. ...
... We now estimate (35). The Q-invariant can also be given a weight by viewing the torus T as sitting inside G 0 and using (26). Namely, ...
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