Dihedral extensions and the Ankeny–Artin–Chowla conjecture

Question

Jensen and Yui (Polynomials with $D_p$ as Galois group J. Number Theory 15, 347–375 (1982)) proved that if $p = 4n+1$ is a regular prime, then there is no normal extension of the rationals with Galois group $D_p$ (dihedral of order $2p$) ramified only at $p$. When I first read it I noticed that such an extension exists if and only if $p$ divides $u$, where $t+u\sqrt{p}$ is the fundamental unit of the real quadratic number field with discriminant $p$ (Ankeny, Artin and Chowla conjectured that this never happens; it is known that this property is equivalent to the divisibility of the Bernoulli number $B_{(p-1)/2}$ by $p$, hence implies that $p$ is irregular).

I recall having seen this result in print a few years later, but can't find it anymore. Can anyone help me?

Answer 1

It appears that my former officemate Andreas Reinhart (University of Graz, Austria) has disproven the Ankeny–Artin–Chowla conjecture: more precisely, Andreas has found that $$ d := 331914313984493$$ is a counterexample to the conjecture, see A counterexample to the Conjecture of Ankeny, Artin and Chowla (especially Theorem 2.3) for further details. This is not exactly an answer to the OP, but seems relevant nonetheless.

Answer 2

As I am currently writing up my thesis in English I noticed that I had referred to this result in the preface. It appears as Proposition 1 in an article by Nakagoshi. See also the recent article by Cohen and Thorne.