Functiones et Approximatio Commentarii Mathematici

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

Loïc Grenié and Giuseppe Molteni

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Abstract

We have recently proved several explicit versions of the prime ideal theorem under GRH. Here we further explore the method, in order to deduce its strongest consequence for the case where $x$ diverges.

Article information

Source
Funct. Approx. Comment. Math., Volume 57, Number 1 (2017), 21-38.

Dates
First available in Project Euclid: 5 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.facm/1493949622

Digital Object Identifier
doi:10.7169/facm/1611

Mathematical Reviews number (MathSciNet)
MR3704223

Zentralblatt MATH identifier
06864161

Subjects
Primary: 11R42: Zeta functions and $L$-functions of number fields [See also 11M41, 19F27]
Secondary: 11Y70: Values of arithmetic functions; tables

Keywords
prime ideal theorem Dedekind functions explicit bounds GRH

Citation

Grenié, Loïc; Molteni, Giuseppe. Explicit versions of the prime ideal theorem for Dedekind zeta functions under GRH, II. Funct. Approx. Comment. Math. 57 (2017), no. 1, 21--38. doi:10.7169/facm/1611. https://projecteuclid.org/euclid.facm/1493949622


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References

  • L. Grenié, G. Molteni, Explicit smoothed prime ideals theorems under GRH, Math. Comp. 85 (2016), no. 300, 1875–1899.
  • L. Grenié, G. Molteni, Explicit versions of the prime ideal theorem for Dedekind zeta functions under GRH, Math. Comp. 85 (2016), no. 298, 889–906.
  • J.C. Lagarias, A.M. Odlyzko, Effective versions of the Chebotarev density theorem, Algebraic number fields: $L$-functions and Galois properties (Proc. Sympos., Univ. Durham, Durham, 1975), Academic Press, London, 1977, pp. 409–464.
  • A.M. Odlyzko, Discriminant bounds, http://www.dtc.umn.edu/~odlyzko/unpublished/index.html, 1976.
  • The PARI Group, Bordeaux, megrez number field tables, 2008, Package nftables.tgz from \raggedright http://pari.math.u-bordeaux.fr/packages.html.
  • The PARI Group, Bordeaux, PARI/GP, version 2.6.0, 2013, from http://pari.math.u-bordeaux.fr/.
  • B. Winckler, Théorème de Chebotarev effectif, arxiv:1311.5715, http://arxiv.org/pdf/1311.5715v1.pdf, 2013.