An improved upper bound for the error in the zero-counting formulae for Dirichlet LL-functions and Dedekind zeta-functions

This paper contains new explicit upper bounds for the number of zeroes of Dirichlet L-functions and Dedekind zeta-functions in rectangles.Comment: 13 pages, 2 tables. To appear in Math. Com

An improved upper bound for the error in the zero-counting formulae for Dirichlet L-functions and Dedekind zeta-functions

This paper contains new explicit upper bounds for the number of zeroes of Dirichlet L-functions and Dedekind zeta-functions in rectangles.Supported by Australian Research Council DECRA Grant DE12010017

Zeros of Dedekind zeta functions under GRH

Assuming GRH, we prove an explicit upper bound for the number of zeros of a Dedekind zeta function having imaginary part in $[T-a,T+a]$. We also prove a bound for the multiplicity of the zeros.Comment: Some misprints corrected, simplified proof for a lemma. This version will appear in Mathematics of Computatio

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

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.Comment: Some misprints corrected. This is the final version which will appear in Mathematics of Computatio

Explicit zero density theorems for Dedekind zeta functions

This article studies the zeros of Dedekind zeta functions. In particular, we establish a smooth explicit formula for these zeros and we derive an effective version of the Deuring-Heilbronn phenomenon. In addition, we obtain an explicit bound for the number of zeros in a box.Comment: 24 page