Explicit versions of the prime ideal theorem for Dedekind zeta functions under GRH

Grenié, Loïc; Molteni, Giuseppe

doi:10.1090/mcom3031

Explicit versions of the prime ideal theorem for Dedekind zeta functions under GRH
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by Loïc Grenié and Giuseppe Molteni PDF

Math. Comp. 85 (2016), 889-906 Request permission

Abstract:

Let $\psi _{\mathbb {K}}$ be the Chebyshev function of a number field $\mathbb {K}$. Under the Generalized Riemann Hypothesis we prove an explicit upper bound for $|\psi _{\mathbb {K}}(x)-x|$ in terms of the degree and the discriminant of $\mathbb {K}$. The new bound improves significantly on previous known results.

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