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Search: All articles in the CJM digital archive with keyword Fibonacci numbers

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1. CJM 2010 (vol 63 pp. 241)

Essouabri, Driss; Matsumoto, Kohji; Tsumura, Hirofumi
 Multiple Zeta-Functions Associated with Linear Recurrence Sequences and the Vectorial Sum Formula We prove the holomorphic continuation of certain multi-variable multiple zeta-functions whose coefficients satisfy a suitable recurrence condition. In fact, we introduce more general vectorial zeta-functions and prove their holomorphic continuation. Moreover, we show a vectorial sum formula among those vectorial zeta-functions from which some generalizations of the classical sum formula can be deduced. Keywords:Zeta-functions, holomorphic continuation, recurrence sequences, Fibonacci numbers, sum formulasCategories:11M41, 40B05, 11B39

2. CJM 2003 (vol 55 pp. 711)

Broughan, Kevin A.
 Adic Topologies for the Rational Integers A topology on \$\mathbb{Z}\$, which gives a nice proof that the set of prime integers is infinite, is characterised and examined. It is found to be homeomorphic to \$\mathbb{Q}\$, with a compact completion homeomorphic to the Cantor set. It has a natural place in a family of topologies on \$\mathbb{Z}\$, which includes the \$p\$-adics, and one in which the set of rational primes \$\mathbb{P}\$ is dense. Examples from number theory are given, including the primes and squares, Fermat numbers, Fibonacci numbers and \$k\$-free numbers. Keywords:\$p\$-adic, metrizable, quasi-valuation, topological ring,, completion, inverse limit, diophantine equation, prime integers,, Fermat numbers, Fibonacci numbersCategories:11B05, 11B25, 11B50, 13J10, 13B35