منابع مشابه
Euclid’s Algorithm in Quartic Cm-fields
In this note we present techniques to compute inhomogeneous minima of norm forms; as an application, we determine all norm-Euclidean complex bicyclic quartic number fields.
متن کاملClass Numbers of Orders in Quartic Fields
as x → ∞, where L(x) is the function L(x) = ∫ x 1 e t dt. Sarnak established this result by identifying the regulators with lengths of closed geodesics of the modular curve SL2(Z)\H, where H denotes the upper half-plane, and using the Prime Geodesic Theorem for this Riemannian surface. Actually Sarnak proved not this result but the analogue where h(O) is replaced by the class number in the narr...
متن کاملClass Invariants for Quartic Cm Fields
One can define class invariants for a quartic primitive CM field K as special values of certain Siegel (or Hilbert) modular functions at CM points corresponding to K. Such constructions were given in [DSG] and [Lau]. We provide explicit bounds on the primes appearing in the denominators of these algebraic numbers. This allows us, in particular, to construct S-units in certain abelian extensions...
متن کاملExceptional elliptic curves over quartic fields
We study the number of elliptic curves, up to isomorphism, over a fixed quartic field K having a prescribed torsion group T as a subgroup. Let T = Z/mZ ⊕ Z/nZ, where m|n, be a torsion group such that the modular curve X1(m,n) is an elliptic curve. Let K be a number field such that there is a positive and finite number of elliptic curves E over K having T as a subgroup. We call such pairs (T,K) ...
متن کاملClass Invariants for Quartic CM Fields
— One can define class invariants for a quartic primitive CM field K as special values of certain Siegel (or Hilbert) modular functions at CM points corresponding to K. Such constructions were given by de Shalit-Goren and Lauter. We provide explicit bounds on the primes appearing in the denominators of these algebraic numbers. This allows us, in particular, to construct S-units in certain abeli...
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ژورنال
عنوان ژورنال: International Mathematical Forum
سال: 2006
ISSN: 1314-7536
DOI: 10.12988/imf.2006.06174