A note on elasticity of factorizations (Q1804188)

Let \(K\) be an algebraic number field, \(R\) its ring of integers, and \(H\) its class group. For any element \(a\) of \(R\), denote by \(f(a)\) the ratio \(m/n\), where \(m\), \(n\) are the maximal resp. the minimal number of factors in a factorization of \(a\) into irreducibles. In a recent paper, \textit{R. J. Valenza} [J. Number Theory 36, No. 2, 212-218 (1990; Zbl 0721.11043)] investigated the quantity \(\rho (K)= \sup\{ f(a)\): \(a\in R\}\). The present author shows that \(\rho(K)= D(H)/2\), where \(D(H)\) is the Davenport constant of the group \(H\).