We study the group of automorphisms of Shimura curves X0(D, N) attached to an Eichler order of square-free level N in an indefinite rational quaternion algebra of discriminant D > 1. We prove that,â€¦ (More)

We consider the generation of prime order elliptic curves (ECs) over a prime field Fp using the Complex Multiplication (CM) method. A crucial step of this method is to compute the roots of a specialâ€¦ (More)

Complex Multiplication (CM) method is a frequently used method for the generation of prime order elliptic curves (ECs) over a prime field Fp. The most demanding and complex step of this method is theâ€¦ (More)

We consider the generation of prime-order elliptic curves (ECs) over a prime field $\mathbb{F}_{p}$ using the Complex Multiplication (CM) method. A crucial step of this method is to compute the rootsâ€¦ (More)

We use rigid analytic uniformization by Schottky groups to give a bound for the order of the abelian subgroups of the automorphism group of a Mumford curve in terms of its genus.

A theorem of Tate and Turner says that global function fields have the same zeta function if and only if the Jacobians of the corresponding curves are isogenous. In this note, we investigate whatâ€¦ (More)

All compact Riemann surfaces (visa-vis complex projective curves) of genus g 2 share the same universal topological covering space, and hence admit a uniformization by a discrete subgroup ofâ€¦ (More)

We apply the known results on the Galois module structure of the sheaf of polydifferentials in order to study the dimension of the tangent space of the deformation functor of curves withâ€¦ (More)

Shimura reciprocity law allows us to verify that a modular function gives rise to a class invariant. Here we present a new method based on Shimura reciprocity that allows us not only to verify but toâ€¦ (More)