The results of [2] on the congruence of Ankeny-Artin-Chowla type modulo p² for real subfields of of a prime degree l is simplified. This is done on the basis of a congruence for the Gauss period (Theorem 1). The results are applied for the quadratic field ℚ(√p), p ≡ 5 (mod 8) (Corollary 1).
@article{bwmeta1.element.bwnjournal-article-aav85i4p377bwm,
author = {Stanislav Jakubec},
title = {Note on the congruence of Ankeny-Artin-Chowla type modulo p$^2$},
journal = {Acta Arithmetica},
volume = {84},
year = {1998},
pages = {377-388},
zbl = {0912.11041},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav85i4p377bwm}
}
Stanislav Jakubec. Note on the congruence of Ankeny-Artin-Chowla type modulo p². Acta Arithmetica, Tome 84 (1998) pp. 377-388. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav85i4p377bwm/
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[001] [2] S. Jakubec, Congruence of Ankeny-Artin-Chowla type modulo p² for cyclic fields of prime degree l, Acta Arith. 74 (1996), 293-310. | Zbl 0853.11086
[002] [3] S. Jakubec, The congruence for Gauss's period, J. Number Theory 48 (1994), 36-45. | Zbl 0807.11049
[003] [4] S. Jakubec, On Vandiver's conjecture, Abh. Math. Sem. Univ. Hamburg 64 (1994), 105-124. | Zbl 0828.11059