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Resolution of T. Ward's question and the Israel-Finch conjecture: Precise analysis of an integer sequence arising in dynamics

par Gaither, Jeffrey B.;Louchard, Guy ;Wagner, Stephan;Ward, Mark Daniel
Référence Combinatorics, probability & computing, 24, 1, page (195-215)
Publication Publié, 2015

Article révisé par les pairs

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Résumé :

We analyse the first-order asymptotic growth of an = ∫10∏nj=1 4 sin2(πjx) dx. The integer an appears as the main term in a weighted average of the number of orbits in a particular quasihyperbolic automorphism of a 2n-torus, which has applications to ergodic and analytic number theory. The combinatorial structure of an is also of interest, as the 'signed' number of ways in which 0 can be represented as the sum of ∈j j for ?n ≤ j ≤ n (with j ≠ 0), with ∈j ∈ {0, 1}. Our result answers a question of Thomas Ward (no relation to the fourth author) and confirms a conjecture of Robert Israel and Steven Finch. Copyright © 2014 Cambridge University Press.