4 citations · 8 across the 7 of their papers we have counts for
7 papers
Theta relations with real multiplication by sqrt(3)
Robert Carls
In this article we compute new theta relations which define the moduli space of abelian surfaces with real multiplication by square root three. We give the locus of square root thr…
Fast point counting on genus two curves in characteristic three
Robert Carls
In this article we give the details of an effective point counting algorithm for genus two curves over finite fields of characteristic three. The algorithm has an application in th…
Explicit Frobenius lifts on elliptic curves
Robert Carls
In this article we give explicit formulae for a lift of the relative Frobenius morphism between elliptic curves and show how one can compute this lift in the case of ordinary reduc…
A p-adic quasi-quadratic point counting algorithm
Robert Carls, David Lubicz
In this article we give an algorithm for the computation of the number of rational points on the Jacobian variety of a generic ordinary hyperelliptic curve defined over a finite fi…
Higher dimensional 3-adic CM construction
R. Carls, D. Kohel, D. Lubicz
We find equations for the higher dimensional analogue of the modular curve X_0(3) using Mumford's algebraic formalism of algebraic theta functions. As a consequence, we derive a me…
Galois theory of the canonical theta structure
Robert Carls
In this article we give a Galois-theoretic characterization of the canonical theta structure. The Galois property of the canonical theta structure translates into certain -adic…