منابع مشابه
On the heights of algebraic points on curves over number fields
Let X be a semi-stable regular curve over the spectrum S of the integers in a number field F , and L̄ = (L, h) an hermitian line bundle on X , i.e. L is an algebraic line bundle on X and h is a smooth hermitian metric (invariant by complex conjugation) on the restriction of L to the set X(C) of complex points of X . In this paper we are interested in the height hL̄(D) of irreducible divisors D on...
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In this paper, we extend the definition of the Nathanson height from points in projective spaces over Fp to points in projective spaces over arbitrary finite fields. If [a0 : . . . : an] ∈ P(Fp), then the Nathanson height is hp([a0 : a1 : . . . : ad]) = min b∈Fp d ∑ i=0 H(bai) where H(ai) = |N(ai)|+p(deg(ai)−1) with N the field norm and |N(ai)| the element of {0, 1, . . . , p− 1} congruent to N...
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Let O be an order of an algebraic number field. It was shown by Ge that given a factorization of an O-ideal a into a product of O-ideals it is possible to compute in polynomial time an overorder O′ of O and a gcdfree refinement of the input factorization; i.e., a factorization of aO′ into a power product of O′-ideals such that the bases of that power product are all invertible and pairwise copr...
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For an even Dirichlet character , we obtain a formula for L(1;) in terms of a sum of Dirichlet L-series evaluated at s = 2 and s = 3 and a rapidly convergent numerical series involving the central binomial coeecients. We then derive a class number formula for real quadratic number elds by taking L(s;) to be the quadratic L-series associated with these elds.
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1964
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1964-11110-1