Catalan and Apéry numbers in residue classes | Macquarie University ResearchOnline

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Title: Catalan and Apéry numbers in residue classes
Related: Journal of combinatorial theory, series A, Vol. 113, Issue 5, p.851-865
DOI: 10.1016/j.jcta.2005.08.003
Publisher: Academic Press
Date: 2006
Author/Creator: Garaev, Moubariz Z
Author/Creator: Luca, Florian
Author/Creator: Shparlinski, Igor E
Description: We estimate character sums with Catalan numbers and middle binomial coefficients modulo a prime p. We use this bound to show that the first at most p^13/2(logp)⁶ elements of each sequence already fall in all residue classes modulo every sufficiently large p, which improves the previously known result requiring p^O(p) elements. We also study, using a different technique, similar questions for sequences satisfying polynomial recurrence relations like the Apéry numbers. We show that such sequences form a finite additive basis modulo p for every sufficiently large prime p.
Description: 15 page(s)
Subject Keyword: Catalan numbers
Subject Keyword: Apéry numbers
Subject Keyword: congruences
Subject Keyword: bounds for character sums
Resource Type: journal article
Organisation: Macquarie University. Dept. of Computing

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