Marcelo Paredes

activity

20192022

most citedUniform bounds for the number of rational points on varieties over global fields

13 citations · 13 across the 2 of their papers we have counts for

collaborators

4 papers

math.NT2022

Effective Hilbert's Irreducibility Theorem for global fields

Marcelo Paredes, Román Sasyk

We prove an effective form of Hilbert's irreducibility theorem for polynomials over a global field $K$ . More precisely, we give effective bounds for the number of specializations $…

math.NT2021★ 13 cited

Uniform bounds for the number of rational points on varieties over global fields

Marcelo Paredes, Román Sasyk

We extend the work of Salberger; Walsh; Castryck, Cluckers, Dittmann and Nguyen; and Vermeulen to prove the uniform dimension growth conjecture of Heath-Brown and Serre for varieti…

math.NT2019

The inverse sieve problem for algebraic varieties over global fields

Juan Manuel Menconi, Marcelo Paredes, Román Sasyk

Let $K$ be a global field and let $Z$ be a geometrically irreducible algebraic variety defined over $K$ . We show that if a big set $S \subseteq Z$ of rational points of bounded heig…

math.NT2019

Ill-distributed sets over global fields and exceptional sets in Diophantine Geometry

Marcelo Paredes

Let $K \subseteq R$ be a number field. Using techniques of discrete analysis, we prove that for definable sets $X$ in $R_{e x p}$ of dimension at most $2$ a conject…