Papers › Order bounds for C²-finite sequences
Order bounds for C²-finite sequences
Manuel Kauers, Philipp Nuspl, Veronika Pillwein
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
A sequence is called C-finite if it satisfies a linear recurrence with constant coefficients. We study sequences which satisfy a linear recurrence with C-finite coefficients. Recently, it was shown that such C²-finite sequences satisfy similar closure properties as C-finite sequences. In particular, they form a difference ring. In this paper we present new techniques for performing these closure properties of C²-finite sequences. These methods also allow us to derive order bounds which were not known before. Additionally, they provide more insight in the effectiveness of these computations. The results are based on the exponent lattice of algebraic numbers. We present an iterative algorithm which can be used to compute bases of such lattices.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections