E. Mulder

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20232026

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math.NT2026

Multi-target hyperbolic sieves and elliptic trace obstructions

Pantelimon Stănică, Erik Mulder, Markus Hittmeir

Let $N = pq$ be a semiprime and let $ℓ ∤ N a$ be an odd prime. The hyperbolic sieve set $H_{a} (N; ℓ) = {a x + N x^{- 1} : x \in F_{ℓ}^{*}}$ contains the residue of the linear form…

math.NT2025

Large smooth twins from short lattice vectors

Erik Mulder, Bruno Sterner, Wessel van Woerden

Finding the largest pair of consecutive $B$ -smooth integers is computationally challenging. Current algorithms to find such pairs have an exponential runtime -- which has only be p…

math.NT2023

Fast square-free decomposition of integers using class groups

Erik Mulder

Let $n = a^{2} b$ , where $b$ is square-free. In this paper we present an algorithm based on class groups of binary quadratic forms that finds the square-free decomposition of $n$ , i.e.…