From the Ideal Theorem to the class number

TL;DR

This paper derives an explicit upper bound for a key class number-related quantity in number theory, based on an effective constant in the Ideal Theorem's error term.

Contribution

It provides a new explicit upper bound for class number-related quantities using an effective constant in the Ideal Theorem's error term.

Findings

Established an explicit upper bound for $h_K \\mathcal{R}_K d_K^{-1/2}$.

Connected the bound to an effective constant in the Ideal Theorem.

Enhanced understanding of class number estimates in algebraic number theory.

Abstract

In this note, we provide an explicit upper bound for $h_K \mathcal{R}_K d_K^{-1/2}$ which depends on an effective constant in the error term of the Ideal Theorem.