# Note on the congruence of Ankeny-Artin-Chowla type modulo p²

Acta Arithmetica (1998)

- Volume: 85, Issue: 4, page 377-388
- ISSN: 0065-1036

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topStanislav Jakubec. "Note on the congruence of Ankeny-Artin-Chowla type modulo p²." Acta Arithmetica 85.4 (1998): 377-388. <http://eudml.org/doc/207175>.

@article{StanislavJakubec1998,

abstract = {The results of [2] on the congruence of Ankeny-Artin-Chowla type modulo p² for real subfields of $ℚ(ζ_p)$ 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).},

author = {Stanislav Jakubec},

journal = {Acta Arithmetica},

keywords = {cyclic extension; Ankeny-Artin-Chowla congruence; Gaussian period; quadratic field},

language = {eng},

number = {4},

pages = {377-388},

title = {Note on the congruence of Ankeny-Artin-Chowla type modulo p²},

url = {http://eudml.org/doc/207175},

volume = {85},

year = {1998},

}

TY - JOUR

AU - Stanislav Jakubec

TI - Note on the congruence of Ankeny-Artin-Chowla type modulo p²

JO - Acta Arithmetica

PY - 1998

VL - 85

IS - 4

SP - 377

EP - 388

AB - The results of [2] on the congruence of Ankeny-Artin-Chowla type modulo p² for real subfields of $ℚ(ζ_p)$ 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).

LA - eng

KW - cyclic extension; Ankeny-Artin-Chowla congruence; Gaussian period; quadratic field

UR - http://eudml.org/doc/207175

ER -

## References

top- [1] E. R. Hansen, A Table of Series and Products, Prentice-Hall, 1973.
- [2] S. Jakubec, Congruence of Ankeny-Artin-Chowla type modulo p² for cyclic fields of prime degree l, Acta Arith. 74 (1996), 293-310. Zbl0853.11086
- [3] S. Jakubec, The congruence for Gauss's period, J. Number Theory 48 (1994), 36-45. Zbl0807.11049
- [4] S. Jakubec, On Vandiver's conjecture, Abh. Math. Sem. Univ. Hamburg 64 (1994), 105-124. Zbl0828.11059

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