منابع مشابه
Counting discriminants of number fields
For each transitive permutation group G on n letters with n ≤ 4, we give without proof results, conjectures, and numerical computations on discriminants of number fields L of degree n over Q such that the Galois group of the Galois closure of L is isomorphic to G.
متن کاملSquare-free discriminants of Frobenius rings
Let E be an elliptic curve over Q. It is well known that the ring of endomorphisms of Ep, the reduction of E modulo a prime p of ordinary reduction, is an order of the quadratic imaginary field Q(πp) generated by the Frobenius element πp. When the curve has complex multiplication (CM), this is always a fixed field as the prime varies. However, when the curve has no CM, very little is known, not...
متن کاملCounting Squarefree Discriminants of Trinomials under Abc
For an odd positive integer n ≥ 5, assuming the truth of the abc conjecture, we show that for a positive proportion of pairs (a, b) of integers the trinomials of the form tn + at + b (a, b ∈ Z) are irreducible and their discriminants are squarefree.
متن کاملCounting Square-Free Numbers
The main topic of this contribution is the problem of counting square-free numbers not exceeding n. Before this work we were able to do it in time Õ( √ n). Here, the algorithm with time complexity Õ(n) and with memory complexity Õ(n) is presented. Additionally, a parallel version is shown, which achieves full scalability. As of now the highest computed value was for n = 10. Using our implementa...
متن کاملA-Discriminants for Complex Exponents and Counting Real Isotopy Types
We take a first step toward extending the theory of A-discriminants, and Kapranov’s parametrization of A-discriminant varieties [Kap91], to a broader family of functions including polynomials as a very special case. As an application, we prove a quadratic upper bound on the number of isotopy types of real zero sets of certain n-variate exponential sums, in a setting where the best previous boun...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2016
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2015.10.015