A propos d'une conjecture arithmétique sur le groupe de Chow d'une surface rationnelle
A pure arithmetical characterization for certain fields with a given class group
A pure arithmetical definition of the class group
A purely algebraic proof of special cases of Tchebotarev's theorem
A quadratic field of prime discriminant requiring three generators for its class group, and related theory
A quadratic field which is euclidean but not norm-euclidean.
A quantitative aspect of non-unique factorizations: the Narkiewicz constants III
Let K be an algebraic number field with non-trivial class group G and be its ring of integers. For k ∈ ℕ and some real x ≥ 1, let denote the number of non-zero principal ideals with norm bounded by x such that a has at most k distinct factorizations into irreducible elements. It is well known that behaves for x → ∞ asymptotically like . We prove, among other results, that for all integers n₁,n₂ with 1 < n₁|n₂.
A quantitative aspect of non-unique factorizations: the Narkiewicz constants II
Let K be an algebraic number field with non-trivial class group G and be its ring of integers. For k ∈ ℕ and some real x ≥ 1, let denote the number of non-zero principal ideals with norm bounded by x such that a has at most k distinct factorizations into irreducible elements. It is well known that behaves, for x → ∞, asymptotically like . In this article, it is proved that for every prime p, , and it is also proved that if and m is large enough. In particular, it is shown that for...
A question on the discriminants of involutions of central division algebras.
A Rankin-Selberg integral for the adjoint representation of GL3.
A reciprocity law for K2-traces.
A relation between automorphic representations of and
A relative integral basis over for the normal closure of a pure cubic field.
A relative trace formula
A remark about isogenies of elliptic curves over quadratic fields
A remark about zeta functions of number fields of prime degree.
A remark on arithmetic equivalence and the normset
1. Introduction. Number fields with the same zeta function are said to be arithmetically equivalent. Arithmetically equivalent fields share much of the same properties; for example, they have the same degrees, discriminants, number of both real and complex valuations, and prime decomposition laws (over ℚ). They also have isomorphic unit groups and determine the same normal closure over ℚ [6]. Strangely enough, it has been shown (for example [4], or more recently [6] and [7]) that this does...
A remark on certain Hecke L-series which are non-negative on the real axis
A remark on Construire un noyau de la fonctorialité by Lafforgue
Lafforgue has proposed a new approach to the principle of functoriality in a test case, namely, the case of automorphic induction from an idele class character of a quadratic extension. For technical reasons, he considers only the case of function fields and assumes the data is unramified. In this paper, we show that his method applies without these restrictions. The ground field is a number field or a function field and the data may be ramified.
A remark on Hilbert's Theorem 92