Values of the dedekind eta function at quadratic irrationalities (vol 53, pg 434, 2001)

Habib Muzaffar of Carleton University has pointed out to the authors that i n their paper [A] only the result pi (K,d)(x) + pi (K-1,d)(x) = 1/h(d) x/log x + O-K,O-d(x/log(2)x) follows from the prime ideal theorem with remainder for ideal classes, and not the stronger result pi (K,d)(x) = 1/2h(d) x/log x + O-K,O-d(x/log(2)x) stated in Lemma 5.2. This necessitates changes in Sections 5 and 6 of [A]. The main results of the paper are not affected by these changes. It should also be noted that, starting on page 177 of [A], each and every occurrence of o(s - 1) should be replaced by o(1). Sections 5 and 6 of [A] have been r ewritten to incorporate the above mentioned correction and are given below. They should replace the original Sections 5 and 6 of [A].