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

• Autorzy: Stanislav Jakubec
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 11R29: Class numbers, class groups, discriminants

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1998
• Tom: 85
• Numer: 4
• Strony: 377-388

Daty

wydano

1998

otrzymano

1997-11-14

Twórcy

autor

Stanislav Jakubec

• Matematický ústav SAV, Štefánikova 49, 814 73 Bratislava, Slovakia

Bibliografia

• [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.
• [3] S. Jakubec, The congruence for Gauss's period, J. Number Theory 48 (1994), 36-45.
• [4] S. Jakubec, On Vandiver's conjecture, Abh. Math. Sem. Univ. Hamburg 64 (1994), 105-124.