Narrow class group
WitrynaNarrow class group is a(n) research topic. Over the lifetime, 25 publication(s) have been published within this topic receiving 165 citation(s). Popular works include A sharp upper bound for the $2$-torsion of class groups of multiquadratic fields., On $2$-Selmer groups and quadratic twists of elliptic curves and more. Witryna1.1 Class group heuristics The Cohen–Lenstra–Martinet–Malle heuristics which were developed in a series of ground-breaking works [13, 15, 16, 14, 28], constitute our best conjectural description of the distribution of the p∞- part of the class group, Cl(K)[p∞], over families of number fields K of fixed degree and signature ordered by …
Narrow class group
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Witryna1 gru 2015 · Fundamental units with norm. −. 1. in real quadratic fields. If we have distinct primes p ≡ q ≡ 1 ( mod 4), with Legendre ( p q) = ( q p) = − 1, there is a solution to u 2 − p q v 2 = − 1 in integers and the fundamental unit of O Q ( p q) has norm − 1. Stevenhagen attributes this to Dirichlet (1834). WitrynaA ray class field of K is the abelian extension of K associated to a ray class group by class field theory, and its Galois group is isomorphic to the corresponding ray class group. The proof of existence of a ray class field of a given ray class group is long and indirect and there is in general no known easy way to construct it (though ...
Witryna370 groups. We also give a numerical example in which k is a sextic field, showing that one can sometimes avoid having to find z E K by computing instead inside a narrow … Witryna28 lis 2024 · Correspondence between class group of binary quadratic forms and the narrow class group via Dirichlet composition: an elementary approach? Ask …
WitrynaGroup-theoretic properties of and the efficient computation of have attracted much attention in recent years. It turns out that the abelian group of cla sses of primitive binary quadratic forms of discriminant is isomorphic to the narrow class group + ,wheretheinterplay ↔ was described earlier. In particular, Gaussian composition of … Witryna7 sie 2024 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site
Witryna24 lut 2014 · Given any family of cubic fields defined by local conditions at finitely many primes, we determine the mean number of 2-torsion elements in the class groups and narrow class groups of these cubic fields when ordered by their absolute discriminants. For an order $\\cal O$ in a cubic field, we study the three groups: $\\rm Cl_2(\\cal …
WitrynaCLASS GROUPS, TOTALLY POSITIVE UNITS, AND SQUARES H. M. EDGAR, R. A. MOLLIN1 AND B. L. PETERSON Abstract. Given a totally real algebraic number field K, we investigate when totally positive units, U¿, are squares, u£. In particular, we prove that the rank of U¿ /Ují is bounded above by the minimum of (1) the 2-rank of the … create your password是什么意思Witryna17 lis 2024 · We also find that monogenicity has an increasing effect on the average number of non-trivial $2$-torsion elements in the narrow class group. In addition, we obtain unconditional statements for monogenised rings of odd degree. For an order $\mathcal{O}$, denote by $\mathcal{I}_2(\mathcal{O})$ the group of $2$-torsion … do baby rabbits need alfalfa hayWitrynaNarrow class group is a(n) research topic. Over the lifetime, 25 publication(s) have been published within this topic receiving 165 citation(s). Popular works include Dyadic ideal, class group, and tame kernel in quadratic fields, Higher genus theory and more. create your password什么意思WitrynaThe output is a 3-component row vector v analogous to the corresponding class group component bnf.clgp: the first component is the narrow class number v.no, the second component is a vector containing the SNF cyclic components v.cyc of the narrow class group, and the third is a vector giving the generators of the corresponding v.gen … create your passwordWitrynaOn page 103, he proves that the narrow class group you ask about is isomorphic to the class group of binary quadratic forms. On page 82, Buell points out that … create your own zip hoodieWitrynaOn page 103, he proves that the narrow class group you ask about is isomorphic to the class group of binary quadratic forms. On page 82, Buell points out that computations show about 80 percent of positive prime discriminants have class number one. Note these primes are $1 \pmod 4.$ And it is certainly conjectured that the list is infinite. do baby rabbits need a heat lampWitrynainformation about the etale fundamental group by computing the narrow class group! Example 3. K = Q. Each fractional ideal of Q can be generated by a positive rational … do baby rabbits have teeth