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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).

Note on the congruences $2^{p - 1} \equiv 1 (mod p^{2})$ , $3^{p - 1} \equiv 1 (mod p^{2})$ , $5^{p - 1} \equiv 1 (mod p^{2})$

Stanislav Jakubec (1998)

Acta Mathematica et Informatica Universitatis Ostraviensis

Note on the cubic residues

Stanislav Jakubec (1997)

Acta Mathematica et Informatica Universitatis Ostraviensis

Note on the fractional parts of λθⁿ

Masayoshi Hata (2005)

Acta Arithmetica

Note on the Galois module structure of quadratic extensions

Günter Lettl (1994)

Colloquium Mathematicae

In this note we will determine the associated order of relative extensions of algebraic number fields, which are cyclic of prime order p, assuming that the ground field is linearly disjoint to the pth cyclotomic field, $ℚ^{(p)}$ . For quadratic extensions we will furthermore characterize when the ring of integers of the extension field is free over the associated order. All our proofs are quite elementary. As an application, we will determine the Galois module structure of $ℚ^{(n)} / ℚ^{{(n)}^{+}}$ .

Note on the Hilbert 2-class field tower

Abdelmalek Azizi, Mohamed Mahmoud Chems-Eddin, Abdelkader Zekhnini (2022)

Mathematica Bohemica

Let $k$ be a number field with a 2-class group isomorphic to the Klein four-group. The aim of this paper is to give a characterization of capitulation types using group properties. Furthermore, as applications, we determine the structure of the second 2-class groups of some special Dirichlet fields $𝕜 = ℚ (\sqrt{d}, \sqrt{- 1})$ , which leads to a correction of some parts in the main results of A. Azizi and A. Zekhini (2020).

Note on the jacobi sum $J (χ, χ)$

Stanislav Jakubec (1995)

Journal de théorie des nombres de Bordeaux

Notes on an analogue of the Fontaine-Mazur conjecture

Jeffrey D. Achter, Joshua Holden (2003)

Journal de théorie des nombres de Bordeaux

We estimate the proportion of function fields satisfying certain conditions which imply a function field analogue of the Fontaine-Mazur conjecture. As a byproduct, we compute the fraction of abelian varieties (or even jacobians) over a finite field which have a rational point of order $ℓ$ .

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Note on an index formula of elliptic units in a ring class field II

Note on an index formula of elliptic units in a ring class field

Note on class groups of algebraic function fields.

Note on primes of type x2 + 32y2, class number, and residuacity.

Note on the class-number of the maximal real subfield of a cyclomatic field.

Note on the class-number of the maximal real subfield of a cyclomatic field.

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

Note on the congruences $2^{p - 1} \equiv 1 (mod p^{2})$ , $3^{p - 1} \equiv 1 (mod p^{2})$ , $5^{p - 1} \equiv 1 (mod p^{2})$

Note on the cubic residues

Note on the fractional parts of λθⁿ

Note on the Galois module structure of quadratic extensions

Note on the Hilbert 2-class field tower

Note on the jacobi sum $J (χ, χ)$

Notes on an analogue of the Fontaine-Mazur conjecture

Notes on étale cohomology of number fields

Notes on small class numbers

Notes on the method of Frobenian functions with applications to Fourier coefficients of modular forms

Notions relatives de régulateurs et de hauteurs

Nouveaux exemples d'extension relatives sans base normale

Nouvelles caractérisations des nombres de Pisot et de Salem

Currently displaying 81 – 100 of 110