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arXiv · 1312.4463

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

Loïc Grenié·Giuseppe Molteni
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Abstract

Let $\psi_\K$ be the Chebyshev function of a number field $\K$. Under GRH we prove an explicit upper bound for $|\psi_\K(x)-x|$ in terms of the degree and the discriminant of $\K$. The new bound improves significantly on previous known results.

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Loïc Grenié, Giuseppe Molteni. 2013-12-16. Explicit versions of the prime ideal theorem for Dedekind zeta functions under GRH. https://doi.org/10.1090/mcom3031

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