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Dihedral extensions and the Ankeny - Artin - ChowlaAnkeny–Artin–Chowla conjecture

Jensen and Yui (Polynomials with Dp as Galois groupPolynomials with $D_p$ as Galois group J. Number Theory 15, 347-375347–375 (1982)) proved that if p = 4n+1$p = 4n+1$ is a regular prime, then there is no normal extension of the rationals with Galois group Dp$D_p$ (dihedral of order 2p$2p$) ramified only at p$p$. When I first read it I noticed that such an extension exists if and only if p$p$ divides u$u$, where $t+u\sqrt{p}$ is the fundamental unit of the real quadratic number field with discriminant p $p$ (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$B_{(p-1)/2}$ by p$p$, hence implies that p$p$ is irregular).

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

Dihedral extensions and the Ankeny - Artin - Chowla conjecture

Jensen and Yui (Polynomials with Dp 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 Dp (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?

Dihedral extensions and the Ankeny–Artin–Chowla conjecture

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?

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Franz Lemmermeyer
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Franz Lemmermeyer
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Dihedral extensions and the Ankeny - Artin - Chowla conjecture

Jensen and Yui (Polynomials with Dp 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 Dp (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?