arXiv subjects

Victor Amberger

Publications and source records attributed to Victor Amberger.

2 recordsLinked to original sources

arXiv2025

Bounding the integral of the argument of the Riemann Zeta function

This article improves the estimate of $|S_1(t_2)-S_1(t_1)|$, which is the definite integral of the argument of the Riemann zeta-function between $t_1$ and $t_2$. Estimates of this quantity are needed to apply Turing's method to compute the exact number of zeta zeros up to a given height.

math.NT↗

arXiv2025

Estimating the number of zeros of Dedekind zeta-functions

In this article, I derive a new approach to estimate the number of non-trivial zeros of a given Dedekind zeta function with absolute height at most $T\geq1$ counted with multiplicity. The error term in corresponding asymptotic formula improves all previous results, even in the case of the Riemann zeta function.

math.NT↗