AbstractThe current paper considers the question of power bases in the cyclotomic number field Q(ζ), ζp = 1, p an odd prime. The ring of integers is Z[ζ], and there do exist further “non-obvious” generators for this order; specifically we shall see that Z[α] = Z[ζ] for α = ζ + ζ2 + ⋯ + ζ(p−1)2. We conjecture that, up to conjugacy, there can be no further such integral generators, and prove that this is indeed the case in Q(ζ7)
AbstractLet K be a number field, l a prime number, ζl a primitive l-th root of unity and Kz = K(ζl)....
In this essay, we study and comment on two number theoretical applications on prime cyclotomic field...
AbstractLet p be an odd prime, ζ a primitive pth root of unity. It is proved that Π(1 + iζk)k, 1 ≤ k...
AbstractLet p be an odd prime and q=pm, where m is a positive integer. Let ζ be a primitive qth root...
AbstractLet ζ be a primitive 2mth root of unity. We prove that Z[α]=Z[ζ] if and only if α=n±ζi for s...
AbstractLetpbe an odd prime and Opbe the ring of integers in the cyclotomic fieldQ(ζ), whereζis a pr...
AbstractThe current paper considers the question of power bases in the cyclotomic number field Q(ζ),...
We survey the problem of existence and computation of power bases in number fields. 1 Preliminaries ...
RésuméSoit p un nombre premier impair, soit q=pm, où m est un entier positif ; notons ζq une racine ...
AbstractLet p be a prime number. We say that a number field F satisfies the condition (Hp′) when for...
AbstractLet K/Q be a cyclic extension of degree l. Let ZK be the ring of integers of K. We say that ...
AbstractLet p and l be odd primes. As a consequence of a work of Brinkhuis (Math. Ann. 264 (1983), 5...
AbstractLet p be an odd prime and let η be a unit of the ring of integers of the pnth cyclotomic fie...
AbstractLet p be a prime, pα=ef+1 and suppose that x is a generator of GF(pα). Then the cyclotomic n...
For an unramified odd prime p in a totally real field, we prove that a single Hecke L-value of the f...
AbstractLet K be a number field, l a prime number, ζl a primitive l-th root of unity and Kz = K(ζl)....
In this essay, we study and comment on two number theoretical applications on prime cyclotomic field...
AbstractLet p be an odd prime, ζ a primitive pth root of unity. It is proved that Π(1 + iζk)k, 1 ≤ k...
AbstractLet p be an odd prime and q=pm, where m is a positive integer. Let ζ be a primitive qth root...
AbstractLet ζ be a primitive 2mth root of unity. We prove that Z[α]=Z[ζ] if and only if α=n±ζi for s...
AbstractLetpbe an odd prime and Opbe the ring of integers in the cyclotomic fieldQ(ζ), whereζis a pr...
AbstractThe current paper considers the question of power bases in the cyclotomic number field Q(ζ),...
We survey the problem of existence and computation of power bases in number fields. 1 Preliminaries ...
RésuméSoit p un nombre premier impair, soit q=pm, où m est un entier positif ; notons ζq une racine ...
AbstractLet p be a prime number. We say that a number field F satisfies the condition (Hp′) when for...
AbstractLet K/Q be a cyclic extension of degree l. Let ZK be the ring of integers of K. We say that ...
AbstractLet p and l be odd primes. As a consequence of a work of Brinkhuis (Math. Ann. 264 (1983), 5...
AbstractLet p be an odd prime and let η be a unit of the ring of integers of the pnth cyclotomic fie...
AbstractLet p be a prime, pα=ef+1 and suppose that x is a generator of GF(pα). Then the cyclotomic n...
For an unramified odd prime p in a totally real field, we prove that a single Hecke L-value of the f...
AbstractLet K be a number field, l a prime number, ζl a primitive l-th root of unity and Kz = K(ζl)....
In this essay, we study and comment on two number theoretical applications on prime cyclotomic field...
AbstractLet p be an odd prime, ζ a primitive pth root of unity. It is proved that Π(1 + iζk)k, 1 ≤ k...
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