João C. C. Vargas

activity

20202026

collaborators

4 papers

math.NT2026

The least quadratic residue and integers represented by quadratic forms

Kannan Soundararajan, João C. C. Vargas

Let $ℓ (n)$ denote the least non-trivial reduced quadratic residue modulo $n$ ; that is, $ℓ (n)$ denotes the smallest square-free integer $r > 1$ with $(r, n) = 1$ and $r\equiv x^2 \…

math.NT2025

Extreme values of class group $L$ -functions

João C. C. Vargas

We give a lower bound for the maximum value of class group $L$ -functions attached to $Q (- D)$ at the central point and show that this value is on average at least $$…

math.NT2025

Markoff triples and generating pairs of $SL_{2} (F_{p})$

João C. C. Vargas

Consider the level sets of the Markoff equation $M_{k} : x^{2} + y^{2} + z^{2} - x y z - 2 = k .$ The phenomenon of strong approximation, as named by Bourgain, Gamburd, and Sarnak,…

math.NT2020

On Artin's conjecture for pairs of diagonal forms

João C. C. Vargas

Let $p$ be an odd prime and $d = p^{τ} (p - 1)$ . In the spirit of Aritn's conjecture, consider the system of two diagonal forms of degree $d$ in $s$ variables given by \begin{equation*}…

The least quadratic residue and integers represented by quadratic forms

Extreme values of class group L-functions

Markoff triples and generating pairs of SL2​(Fp​)

On Artin's conjecture for pairs of diagonal forms

Extreme values of class group $L$ -functions

Markoff triples and generating pairs of $SL_{2} (F_{p})$