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Nuno Arala Santos

I am a third-year PhD student under the supervision of Dr. Simon Myerson and Dr. Sam Chow.

E-mail address: Nuno.Arala-Santos(at)


Number Theory, especially interactions between Analytic Number Theory and Diophantine Geometry.


I obtained my Bachelor's degree from the University of Porto in 2018. I then did my Master's at the University of Bonn, which I finished in 2020. I wrote my Master's Thesis under the supervision of Prof. Valentin Blomer on the estimation of Representation Numbers of Quadratic Forms using a variant of the Hardy-Littlewood circle method. (For more details see below, under "Writing".)

For more information on my background see my CV.

Papers and Preprints

  1. A maximal extension of the Bloom-Maynard bound for sets with no square differences (2023) (arXiv, .pdf), submitted
  2. Lines of polynomials with alternating Galois group (2022), (arXiv, .pdf), submitted
  3. On the density of a set of primes associated to an Elliptic Curve (2021), (arXiv, .pdf), Journal of Number Theory 243 (2023) 241-255.

Miscellaneous writing

Below are some math-related texts I wrote over the years, for various purposes. Several of them are written in Portuguese. I intend to translate some of those to English at some point in the future.