Results 11 to 20 of about 1,412,537 (346)
On the units of an algebraic number field [PDF]
Illinois Journal of Mathematics, 1965 James Ax
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On the Goldbach problem in an algebraic number field I. [PDF]
, 1960 The famous but yet unsolved problem of Goldbach is to decide whether the following conjecture is true: every even positive rational integer except 2 and 4 will be represented as the sum of two odd prime numbers.
Takayoshi Mitsui
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On the Infrastructure of the Principal Ideal Class of an Algebraic Number Field of Unit Rank One [PDF]
, 1988 Let R be the regulator and let D be the absolute value of the discriminant of an order 0 of an algebraic number field of unit rank 1. It is shown how the infrastructure idea of Shanks can be used to decrease the number of binary operations needed to ...
Johannes Buchmann, H. C. Williams
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On the fundamental number of the algebraic number-field 𝑘(\root𝑝\of𝑚) [PDF]
, 1910 Jacob Westlund
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Theory of cyclic algebras over an algebraic number field [PDF]
Transactions of the American Mathematical Society, 1932 I present this paper for publication to an American journal and in English for the following reason: The theory of linear algebras has been greatly extended through the work of American mathematicians. Of late, German mathematicians have become active in this theory.
H. Hasse
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On a class of ideals in an algebraic number field
Journal of Number Theory, 1970 AbstractLet k be an algebraic number field and let θ be the ring of integers of k. We define for each positive n and each prime ideal p of θ a nonnegative integer rn(p) as follows: if n = Σi = 0tkiqi is the q-adic expansion of n where q = Np, set rn(p) = (n − Σi = 0tki)/(q − 1).
Hiroshi Gunji, Donald L. McQuillan
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On the Units of Algebraic Number Fields
Journal of Number Theory, 1994 AbstractLet K be an algebraic number field and k be a proper subfield of K. Then we have the relations between the relative degree [K : k] and the increase of the rank of the unit groups. Especially, in the case of mth cyclotomic field Q(ζm), we determine the number m such that the increase of the rank of the unit groups is equal to the number of the ...
H. Takeuchi, I. Yamaguchi
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Fuchsian groups and algebraic number fields [PDF]
Transactions of the American Mathematical Society, 1985 Given the signature of a finitely-generated Fuchsian group, we find the minimal extension of the rationals for which there is a Fuchsian group having the required signature, whose matrix entries lie in this field.
C. Maclachlan, P. L. Waterman
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The distribution of the irreducibles in an algebraic number field [PDF]
Journal of the Australian Mathematical Society, 2005 AbstractWe study the distribution of principal ideals generated by irreducible elements in an algebraic number field.
David M. Bradley +3 more
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On Computing the Discriminant of an Algebraic Number Field [PDF]
Mathematics of Computation, 1985 Let f ( x ) f(x) be a monic irreducible polynomial in Z [ x ] {\mathbf {Z}}[x] , and r a root of f ( x ) f(x) in C. Let K be the field Q (
Theresa P. Vaughan
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