651 research outputs found
Ray class fields generated by torsion points of certain elliptic curves
We first normalize the derivative Weierstrass -function appearing in
Weierstrass equations which give rise to analytic parametrizations of elliptic
curves by the Dedekind -function. And, by making use of this
normalization of we associate certain elliptic curve to a given
imaginary quadratic field and then generate an infinite family of ray class
fields over by adjoining to torsion points of such elliptic curve. We
further construct some ray class invariants of imaginary quadratic fields by
utilizing singular values of the normalization of , as the -coordinate
in the Weierstrass equation of this elliptic curve, which would be a partial
result for the Lang-Schertz conjecture of constructing ray class fields over
by means of the Siegel-Ramachandra invariant
On the Csorgo-RĂŠvĂŠsz increments of finite dimensional Gaussian random fields
In this paper, we establish some limit theorems on the combined Csorgo-RĂŠvĂŠsz increments with moduli of continuity for finite dimensional Gaussian random fields under mild conditions, via estimating upper bounds of large deviation probabilities on suprema of the finite dimensional Gaussian random fields.Csorgo-RĂŠvĂŠsz increment; Gaussian process; random field; modulus of continuity; quasi-increasing; regularly varying function; large deviation probability.
Gauss' form class groups and Shimura's canonical models
Let be a positive integer and be a subgroup of
containing . Let be an imaginary
quadratic field and be an order of discriminant
in . Under some assumptions, we show that induces a form class
group of discriminant (or, of order ) and level
if and only if there is a certain canonical model of the modular curve for
defined over a suitably small number field. In this way we can find an
interesting link between two different subjects.Comment: 18 page
Arithmetic properties of orders in imaginary quadratic fields
Let be an imaginary quadratic field. For an order in
and a positive integer , let be the ray class field of
modulo . We deal with various subjects related to
, mainly about Galois representations attached to elliptic
curves with complex multiplication, form class groups and -functions for
orders
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