Mugurel Barcau

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math.NT2026

Iterated extensions and the ramification dichotomy

Mugurel Barcau, VicenÅ£iu PaÅol

Let $K / Q_{p}$ be finite and let $f \in O_{K} [X]$ be monic, of degree at least two, with $f^{'} (X) \in m_{K} O_{K} [X]$ , equivalently $f ˉ \in k [X^{p}]$ . For a co…

math.NT2026

Transversal Difference Numbers in Finite Abelian Quotients

Mugurel Barcau, VicenÅ£iu PaÅol, George C. Å¢urcaÅ

Given $H\leq G$ finite abelian groups, a transversal $T\subseteq G$ for $G/H$ has fixed size $|G/H|$, but its ambient difference support $D(T)=T-T$ can vary with the embe…

math.NT2026

Logarithmic Density of Rank $\geq 1$ and Rank $\geq 2$ Genus-2 Jacobians and Applications to Hyperelliptic Curve Cryptography

Razvan Barbulescu, Mugurel Barcau, Vicentiu Pasol +1

In this work we study quantitative existence results for genus- $2$ curves over $Q$ whose Jacobians have Mordell--Weil rank at least $1$ or $2$ , ordering the curves by the…

Iterated extensions and the ramification dichotomy

Transversal Difference Numbers in Finite Abelian Quotients

Logarithmic Density of Rank ≥1 and Rank ≥2 Genus-2 Jacobians and Applications to Hyperelliptic Curve Cryptography

Logarithmic Density of Rank $\geq 1$ and Rank $\geq 2$ Genus-2 Jacobians and Applications to Hyperelliptic Curve Cryptography