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 \(\mathbb{F}_q[T]\) 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 \(\mathbb{F}_q[T]\).

Lately, I have been interested in Diophantine equations involving Lucas sequences.

Published papers and preprints

• Explicit prime densities for the rank of appearance in Lucas sequences
  Preprint (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