X. Roulleau

activity

20082025

most citedNegative curves on algebraic surfaces

53 citations · 120 across the 41 of their papers we have counts for

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math.NT2025

Number of partitions of modular integers (with an Appendix by P. Deligne)

David Broadhurst, Xavier Roulleau

For integers $n, k, s$ , we give a formula for the number $T (n, k, s)$ of order $k$ subsets of the ring $Z / n Z$ whose sum of elements is $s$ modulo $n$ . To do so, we de…

math.NT2021★ 1 cited

A refinement of Bézout's Lemma, and order 3 elements in some quaternion algebras over $Q$

Donald I. Cartwright, Xavier Roulleau

Given coprime positive integers $d^{'}, d^{''}$ , Bézout's Lemma tells us that there are integers $u, v$ so that $d^{'} u - d^{''} v = 1$ . We show that, interchanging $d^{'}$ and $d^{''}$ if necessary, we ma…

Number of partitions of modular integers (with an Appendix by P. Deligne)

A refinement of Bézout's Lemma, and order 3 elements in some quaternion algebras over Q

A refinement of Bézout's Lemma, and order 3 elements in some quaternion algebras over $Q$