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

Abstract

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

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

References in corpus (2)

• Explicit smoothed prime ideals theorems under GRH
• Théorème de Chebotarev effectif

Cited by in corpus (9)

• Irreducibility of random polynomials of large degree
• An effective Chebotarev density theorem under GRH
• Uniform bounds for the number of rational points on varieties over global fields
• Explicit smoothed prime ideals theorems under GRH
• Effective log-free zero density estimates for automorphic $L$-functions and the Sato-Tate conjecture
• Explicit Short Intervals for Primes in Arithmetic Progressions on GRH
• Zeros of Dedekind zeta functions under GRH
• Explicit upper bounds on the average of Euler-Kronecker constants of narrow ray class fields
• Explicit versions of the prime ideal theorem for Dedekind zeta functions under GRH, II