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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.14/9957
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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<sup>13/2</sup>(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<sup>O(p)</sup> 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
- 010100 Pure Mathematics
- Subject Keyword
- Catalan numbers
- Subject Keyword
- Apéry numbers
- Subject Keyword
- congruences
- Subject Keyword
- bounds for character sums
- Resource Type
- journal article
- Organisation
- Macquarie University. Department of Computing
- Identifier
- http://hdl.handle.net/1959.14/9957
- Identifier
- mq:945
- Identifier
- ISSN:1096-0899
- Identifier
- mq-rm-2006003153
- Language
- eng
- Reviewed
Macquarie University ResearchOnline
