Research Interests

My research lies in both algebraic and analytic number theory. My topics of interest include:

• The density of certain sets of primes in \(\mathbb{Z}\) or \(\mathbb{F}_q[X]\) related to integral sequences.
• The search for explicit (and possibly closed-form) formulas for these density values. This may require the development of algorithms and computational methods for the constants involved.
• The existence of primitive prime divisors in sequences over \(\mathbb{Z}\) or \(\mathbb{F}_q[X]\).

Lately, I have been interested in Wieferich primes and their generalisations to second order recurrent sequences with coefficients in \(\mathbb{F}_q[X]\).

Published papers and preprints

• Explicit prime densities for Lucas sequence rank divisibility
  Accepted for publication (2026), arXiv, PDF
• Divisibility of the multiplicative order modulo monic irreducible polynomials over finite fields
  Journal of Number Theory, 277 (2025), 105–123, journal, arXiv, PDF
• Primitive prime divisors of polynomial Lucas sequences
  Journal of Algebra, 672 (2025), 400–412, journal, arXiv, PDF
• Multinomial Catalan numbers and Lucas analogues
  Journal of Integer Sequences, 26 (2023), Article 23.9.7, journal, arXiv, PDF

Programming

I enjoy programming and writing code in Pari/GP and SageMath to support my research work. Here below are links to GitHub repositories of said programs:

• Pari/GP
• SageMath

Each folder in the repositories corresponds to a paper or preprint.
More programs coming soon.