Explicit smoothed prime ideals theorems under GRH

DOI10.1090/mcom3039zbMath1415.11171arXiv1312.4465OpenAlexW2953109157MaRDI QIDQ2796023

Loïc Grenié, Giuseppe Molteni

Publication date: 23 March 2016

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.4465

zbMATH Keywords

efficient algorithmbound on small-norm prime idealsChebyshev function of number fieldcomputation of residue of Dedekind zeta functionexplicit inequalities for differences

Mathematics Subject Classification ID

Algebraic number theory computations (11Y40) Zeta functions and (L)-functions of number fields (11R42)

Related Items (12)

Recent results about the prime ideal theorem ⋮ Conditional upper bound for the \(k\)-th prime ideal with given Artin symbol ⋮ Fast norm computation in smooth-degree abelian number fields ⋮ On the global determinant method ⋮ PRIMES AND PRIME IDEALS IN SHORT INTERVALS ⋮ Explicit short intervals for primes in arithmetic progressions on GRH ⋮ An explicit Chebotarev density theorem under GRH ⋮ Explicit versions of the prime ideal theorem for Dedekind zeta functions under GRH. II. ⋮ Explicit versions of the prime ideal theorem for Dedekind zeta functions under GRH ⋮ Zeros of Dedekind zeta functions under GRH ⋮ Primes in explicit short intervals on RH ⋮ Lower estimates for the prime ideal of degree one counting function in the Chebotarev density theorem

Uses Software

• PARI/GP
• nftables

Cites Work

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• Explicit Bounds for Some Functions of Prime Numbers
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