Height and Weber’s Class Number Problem
نویسندگان
چکیده
منابع مشابه
The Gauss Higher Relative Class Number Problem
Assuming the 2-adic Iwasawa main conjecture, we find all CM fields with higher relative class number at most 16: there are at least 31 and at most 34 such fields, and exactly one is not abelian. The problem of determining all imaginary quadratic fields K = Q( √ d) of small class number h(K) was first posed in Article 303 of Gauss’ Disquisitiones Arithmeticae. It would take almost 150 years of w...
متن کاملSmall points on a multiplicative group and class number problem
Let V be an algebraic subvariety of a torus Gm →֒ P n and denote by V ∗ the complement in V of the Zariski closure of the set of torsion points of V . By a theorem of Zhang, V ∗ is discrete for the metric induced by the normalized height ĥ. We describe some quantitative versions of this result, close to the conjectural bounds, and we discuss some applications to study of the class group of some ...
متن کاملLenstra-Hurwitz cliques and the class number one problem
Article history: Received 15 January 2015 Received in revised form 5 November 2015 Accepted 5 November 2015 Available online 4 January 2016 Communicated by David Goss MSC: primary 11R04 secondary 20H10
متن کاملPoints of low height on P over number fields and bounds for torsion in class groups
Let K be a number field and ` a positive integer. The main theorem of [3] gives an upper bound for the order of the `-torsion subgroup in the ideal class group ClK of K under the Generalized Riemann Hypothesis, which can be made unconditional in certain special cases (e.g. when K/Q is a quadratic extension and ` = 3.) The main idea is to show that there are many ideal classes which are not `-to...
متن کاملThe Gauss Class Number Problem for Imaginary Quadratic Fields
a result first proved by Heilbronn [H] in 1934. The Disquisitiones also contains tables of binary quadratic forms with small class numbers (actually tables of imaginary quadratic fields of small class number with even discriminant which is a much easier problem to deal with) and Gauss conjectured that his tables were complete. In modern parlance, we can rewrite Gauss’ tables (we are including b...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 2016
ISSN: 1246-7405,2118-8572
DOI: 10.5802/jtnb.965