Some Additional Analytic Results

Part of the CMS Books in Mathematics book series (CMSBM)

By (8.9), it is clear that we can evaluate h Δ for any order \(\mathcal{O}\) of discriminant Δ of \(\mathbb{K}\), once we know the unit index n and \(h_\mathbb{K}\). However, if we refer to Corollary 8.35.1 for determining \(h_\mathbb{K}\), we notice that the expression for L(1, χΔ) is an infinite series. The purpose of this section is to derive a closed-form formula for \(h_\mathbb{K}\). To this end we must first consider some properties of a particular Gauss sum.


Prime Ideal Class Number Critical Line Riemann Hypothesis Dirichlet Character 
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© Springer Science+Business Media, LLC 2009

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