arXiv subjects

Elisavet Konstantinou

Publications and source records attributed to Elisavet Konstantinou.

3 recordsLinked to original sources

arXiv2011

Ramanujan Invariants for discriminants congruent to $\mathbf{5\;mod \;24

In this paper we compute the minimal polynomials of Ramanujan values $27t_n^{-12}$ for discriminants D\equiv5mod24. Our method is based on Shimura Reciprocity Law as which was made computationally explicit by A.Gee and P. Stevenhagen. However, since these Ramanujan values are not class invariants, we present a modification of the above method which can be applied on modular functions that do not necessarily yield class invariants.

math.NT↗

arXiv2008

Introducing Ramanujan's Class Polynomials in the Generation of Prime Order Elliptic Curves

In this paper, we propose the use of Ramanujan class of polynomials for the construction of prime order elliptic curves using the CM-method. We compare (theoretically and experimentally) the efficiency of using this new class against the use of the Weber, $M_{D,l}(x)$ and $M_{D,p_1,p_2}(x)$ polynomials and show that they clearly outweigh all of them in the generation of prime order elliptic curves.

math.NT↗

arXiv2006

Computing polynomials of the Ramanujan $\mathbf{t_n}$ class invariants

We compute the minimal polynomials of the Ramanujan values $t_n$, where $n\equiv 11 \mod 24$, using Shimura reciprocity law. These polynomials can be used for defining the Hilbert class field of the imaginary quadratic field $\mathbb{Q}(\sqrt{-n})$, and have much smaller coefficients than the Hilbert polynomials.

math.NT↗