Bernadette Faye

activity

20172019

collaborators

5 papers

math.NT2019

Separating singular moduli and the primitive element problem

Yuri Bilu, Bernadette Faye, Huilin Zhu

We prove that $∣ x - y ∣ \geq 800 X^{- 4}$ , where $x$ and $y$ are distinct singular moduli of discriminants not exceeding $X$ . We apply this result to the "primitive element problem" for t…

math.NT2018

An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers

Salah E. Rihane, Bernadette Faye, Florian Luca +1

In this paper, we find all solutions of the exponential Diophantine equation $B_{n + 1}^{x} - B_{n}^{x} = B_{m}$ in positive integer variables $(m, n, x)$ , where $B_{k}$ is the $k$ -th term of the…

math.NT2018

Fields generated by sums and products of singular moduli

Bernadette Faye, Antonin Riffaut

We show that the field $Q (x, y)$ , generated by two singular moduli~ $x$ and~ $y$ , is generated by their sum $x + y$ , unless~ $x$ and~ $y$ are conjugate over~ $Q$ , in wh…

math.NT2017

Diophantine Equation with Arithmetic functions and Binary recurrent sequences

Bernadette Faye

This thesis is about the study of Diophantine equations involving binary recurrent sequences with arithmetic functions. Various Diophantine problems are investigated and new result…

cs.CR2017

Extracting a uniform random bit-string over Jacobian of Hyperelliptic curves of Genus $2$

Bernadette Faye

Here, we proposed an improved version of the deterministic random extractors $S E J$ and $P E J$ proposed by R. R. Farashahi in \cite{F} in 2009. By using the Mumford's representation…

Separating singular moduli and the primitive element problem

An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers

Fields generated by sums and products of singular moduli

Diophantine Equation with Arithmetic functions and Binary recurrent sequences

Extracting a uniform random bit-string over Jacobian of Hyperelliptic curves of Genus 2

Extracting a uniform random bit-string over Jacobian of Hyperelliptic curves of Genus $2$