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

Loïc Grenié; Giuseppe Molteni

doi:10.1090/mcom3031

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

Number Theory 2019-05-28 v4

Authors: 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.

Keywords

prime ideal theorem Dedekind zeta function Chebyshev function explicit upper bound generalized Riemann hypothesis number field discriminant

Cite

@article{arxiv.1312.4463,
  title  = {Explicit versions of the prime ideal theorem for Dedekind zeta functions under GRH},
  author = {Loïc Grenié and Giuseppe Molteni},
  journal= {arXiv preprint arXiv:1312.4463},
  year   = {2019}
}

Comments

Some misprints corrected. This is the final version which will appear in Mathematics of Computation

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

Abstract

Keywords

Cite

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