João Campos-Vargas

Research

I am broadly interested in number theory.

• Covering integers by binary quadratic forms

  Joint with K. Soundararajan.

  In preparation.

• Primes of the form x²+dy² and interactions of class groups

  Preprint (2025).

• Crossing probabilities and random multiplicative functions

  Joint with R. Angelo, M. Aymone, O. Klurman, and M. Xu.

  Available on request.

• Extreme values of class group L-functions

  Submitted (2025).

• Markoff triples and generating pairs of SL₂(𝔽_p)

  Undergraduate thesis (2021).

• On Artin’s conjecture for pairs of diagonal forms

  Int. J. Number Theory 18 (2022), no.3.