Results 31 to 40 of about 290 (54)
CM relations in fibered powers of elliptic families
, 2017 Let $E_\lambda$ be the Legendre family of elliptic curves. Given $n$ linearly independent points $P_1,\dots , P_n \in E_\lambda\left(\overline{\mathbb{Q}(\lambda)}\right)$ we prove that there are at most finitely many complex numbers $\lambda_0$ such ...
André +10 more
core +1 more source
Complex Hyperbolic Surfaces of Abelian Type [PDF]
, 2004 2000 Mathematics Subject Classification: 11G15, 11G18, 14H52, 14J25, 32L07.We call a complex (quasiprojective) surface of hyperbolic type, iff – after removing finitely many points and/or curves – the universal cover is the complex two-dimensional unit ...
Holzapfel, R.
core
On Colmez's product formula for periods of CM-abelian varieties
, 2012 Colmez conjectured a product formula for periods of abelian varieties with complex multiplication by a field K, analogous to the standard product formula in algebraic number theory.
Obus, Andrew
core +1 more source
The Galois theory of the lemniscate [PDF]
, 2012 This article studies the Galois groups that arise from division points of the lemniscate. We compute these Galois groups two ways: first, by class field theory, and second, by proving the irreducibility of lemnatomic polynomials, which are analogs of ...
Cox, David A., Hyde, Trevor
core
Ray class fields generated by torsion points of certain elliptic curves [PDF]
, 2010 We first normalize the derivative Weierstrass $\wp'$-function appearing in Weierstrass equations which give rise to analytic parametrizations of elliptic curves by the Dedekind $\eta$-function.
Dong +3 more
core
Construction of class fields over cyclotomic fields
, 2015 Let $\ell$ and $p$ be odd primes. For a positive integer $\mu$ let $k_\mu$ be the ray class field of $k=\mathbb{Q}(e^{2\pi i/\ell})$ modulo $2p^\mu$. We present certain class fields $K_\mu$ of $k$ such that $k_\mu\leq K_\mu\leq k_{\mu+1}$, and find the ...
Koo, Ja Kyung, Yoon, Dong Sung
core +1 more source
On $L$-function of noncommutative tori
, 2018 We introduce an analog of the $L$-function for noncommutative tori. It is proved that such a function coincides with the Hasse-Weil $L$-function of an elliptic curve with complex multiplication.
Nikolaev, Igor
core
Class invariants for quartic CM fields [PDF]
, 2004 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.
Goren, Eyal Z., Lauter, Kristin E.
core +3 more sources
The complexity of class polynomial computation via floating point approximations [PDF]
, 2008 We analyse the complexity of computing class polynomials, that are an important ingredient for CM constructions of elliptic curves, via complex floating point approximations of their roots.
Enge, Andreas
core +3 more sources
N T ] 2 9 O ct 2 01 2 Algebraic points on Shimura curves of Γ 0 ( p )-type
, 2022 Keisuke Arai
semanticscholar +1 more source