Displaying similar documents to “On a binary recurrent sequence of polynomials”

Integral representation of the n -th derivative in de Branges-Rovnyak spaces and the norm convergence of its reproducing kernel

Emmanuel Fricain, Javad Mashreghi (2008)

Annales de l’institut Fourier

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In this paper, we give an integral representation for the boundary values of derivatives of functions of the de Branges–Rovnyak spaces ℋ ( b ) , where b is in the unit ball of H ∞ ( ℂ + ) . In particular, we generalize a result of Ahern–Clark obtained for functions of the model spaces K b , where b is an inner function. Using hypergeometric series, we obtain a nontrivial formula of combinatorics for sums of binomial coefficients. Then we apply this formula to show the norm convergence of reproducing kernel...

Sets of k -recurrence but not ( k + 1 ) -recurrence

Nikos Frantzikinakis, Emmanuel Lesigne, Máté Wierdl (2006)

Annales de l’institut Fourier

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For every k ∈ ℕ , we produce a set of integers which is k -recurrent but not ( k + 1 ) -recurrent. This extends a result of Furstenberg who produced a 1 -recurrent set which is not 2 -recurrent. We discuss a similar result for convergence of multiple ergodic averages. We also point out a combinatorial consequence related to Szemerédi’s theorem.

A new lower bound for ∥ ( 3 / 2 ) k ∥

Wadim Zudilin (2007)

Journal de Théorie des Nombres de Bordeaux

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We prove that, for all integers k exceeding some effectively computable number  K , the distance from ( 3 / 2 ) k to the nearest integer is greater than 0 . 5803 k .