Results 31 to 40 of about 4,819,757 (284)
Bipowers in Number Fields [PDF]
Proceedings of the American Mathematical Society, 1985 The set of all solutions to the Fermat equation is given a structure. This structure is then characterized up to isomorphism in terms of certain subsets of the integers modulo a prime.
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On the strongly ambiguous classes of some biquadratic number fields [PDF]
Mathematica Bohemica, 2016 We study the capitulation of $2$-ideal classes of an infinite family of imaginary bicyclic biquadratic number fields consisting of fields $\Bbbk=\Bbb Q(\sqrt{2pq}, {\rm i})$, where ${\rm i}=\sqrt{-1}$ and $p\equiv-q\equiv1 \pmod4$ are different primes ...
Abdelmalek Azizi +2 more
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Generators and number fields for torsion points of a special elliptic curve [PDF]
Arab Journal of Mathematical Sciences, 2020 Let E be an elliptic curve with Weierstrass form y2=x3−px, where p is a prime number and let E[m] be its m-torsion subgroup. Let p1=(x1,y1) and p2=(x2,y2) be a basis for E[m], then we prove that ℚ(E[m])=ℚ(x1,x2,ξm,y1) in general.
Hasan Sankari, Mustafa Bojakli
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Relative integral basis for algebraic number fields
International Journal of Mathematics and Mathematical Sciences, 1986 At first conditions are given for existence of a relative integral basis for OK≅Okn−1⊕I with [K;k]=n. Then the constrtiction of the ideal I in OK≅Okn−1⊕I is given for proof of existence of a relative integral basis for OK4(m1,m2)/Ok(m3).
Mohmood Haghighi
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Enumerating number fields [PDF]
Annals of Mathematics, 2020 We construct small models of number fields and deduce a better bound for the number of number fields of given degree and bounded discriminant.
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Quaternary quadratic lattices over number fields
, 2018 We relate proper isometry classes of maximal lattices in a totally definite quaternary quadratic space (V,q) with trivial discriminant to certain equivalence classes of ideals in the quaternion algebra representing the Clifford invariant of (V,q).
Dieudonné J. +7 more
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Real quadratic number fields with metacyclic Hilbert $2$-class field tower [PDF]
Mathematica Bohemica, 2019 We begin by giving a criterion for a number field $K$ with 2-class group of rank 2 to have a metacyclic Hilbert 2-class field tower, and then we will determine all real quadratic number fields $\mathbb Q(\sqrt d)$ that have a metacyclic nonabelian ...
Said Essahel, Ahmed Dakkak, Ali Mouhib
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The number of solutions of cubic diagonal equations over finite fields
AIMS Mathematics, 2023 Let $ p $ be a prime, $ k $ be a positive integer, $ q = p^k $, and $ \mathbb{F}_q $ be the finite field with $ q $ elements. Let $ \mathbb{F}_q^* $ be the multiplicative group of $ \mathbb{F}_{q} $, that is $ \mathbb{F}_q^* = \mathbb{F}_{q}\setminus\{0\}
Shuangnian Hu, Rongquan Feng
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PAC fields over number fields [PDF]
Journal de théorie des nombres de Bordeaux, 2008 We prove that if K is a number field and N is a Galois extension of ℚ which is not algebraically closed, then N is not PAC over K.
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Generalized Reed-Solomon codes over number fields and exact gradient coding
AIMS MathematicsThis paper describes generalized Reed-Solomon (GRS) codes over number fields that are invariant under certain permutations. We call these codes generalized quasi-cyclic (GQC) GRS codes.
Irwansyah +3 more
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