On abelian varieties associated with elliptic curves with complex multiplication
On certain reduction problems concerning Abelian surfaces.
On equations defining fake elliptic curves
Shimura curves associated to rational nonsplit quaternion algebras are coarse moduli spaces for principally polarized abelian surfaces endowed with quaternionic multiplication. These objects are also known as fake elliptic curves. We present a method for computing equations for genus 2 curves whose Jacobian is a fake elliptic curve with complex multiplication. The method is based on the explicit knowledge of the normalized period matrices and on the use of theta functions with characteristics. As...
On Siegel modular forms. Part I.
On some equalities for the Weierstrass modular units of level p
On special values of theta functions of genus two
We study a certain finitely generated multiplicative subgroup of the Hilbert class field of a quartic CM field. It consists of special values of certain theta functions of genus 2 and is analogous to the group of Siegel units. Questions of integrality of these specials values are related to the arithmetic of the Siegel moduli space.
On the Conjecture of Birch and Swinnerton-Dyer
On the critical values of Hecke L-functions for imaginary quadratic fields.
On the de Rham and -adic realizations of the elliptic polylogarithm for CM elliptic curves
In this paper, we give an explicit description of the de Rham and -adic polylogarithms for elliptic curves using the Kronecker theta function. In particular, consider an elliptic curve defined over an imaginary quadratic field with complex multiplication by the full ring of integers of . Note that our condition implies that has class number one. Assume in addition that has good reduction above a prime unramified in . In this case, we prove that the specializations of the -adic elliptic...
On the existence of dimension zero divisors in algebraic function fields defined over
On the generalized principal ideal theorem of complex multiplication
In the -th cyclotomic field a prime number, , the prime is totally ramified and the only ideal above is generated by , with the primitive -th root of unity . Moreover these numbers represent a norm coherent set, i.e. . It is the aim of this article to establish a similar result for the ray class field of conductor over an imaginary quadratic number field where is the power of a prime ideal in . Therefore the exponential function has to be replaced by a suitable elliptic function....
On the Iwasawa theory of CM elliptic curves at supersingular primes
On the Periods of Abelian Integrals and a Formula of Chowla and Selberg.
On the square root of special values of certain L-series.
p-Adic L-Functions for CM Fields.
p-adic measures on Galois groups.
Points on X⁺₀(N) over quadratic fields
Primitive points on elliptic curves
Propriétés arithmétiques des dérivées de la fonction modulaire j(...)
Racines cubiques de nombres entiers et multiplication complexe dans les fonctions elliptiques