3 papers
math.NT2025
Deterministic polynomial factorisation modulo many primes
Daniel Altman
Designing a deterministic polynomial time algorithm for factoring univariate polynomials over finite fields remains a notorious open problem. In this paper, we present an unconditi…
math.NT2025
On polynomial progressions via transference
Daniel Altman, Mehtaab Sawhney
We prove new cases of reasonable bounds for the polynomial Szemerédi theorem both over with prime and over the integers. In particular, we prove reason…
math.CO2024
On the uncommonness of minimal rank-2 systems of linear equations
Daniel Altman, Anita Liebenau
We prove that suitably generic pairs of linear equations on an even number of variables are uncommon. This verifies a conjecture of Kamčev, Morrison and the second author. Moreover…