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    22 mars, par (Shalom Eliahou), Shalom Eliahou
    For c ∈ Q, consider the quadratic polynomial map ϕ_c (x) = x^2 − c. Flynn, Poonen and Schaefer conjectured in 1997 that no rational cycle of ϕ_c under iteration has length more than 3. Here we discuss this conjecture using arithmetic and combinatorial means, leading to three main results. First, we (...)
  • [hal-00649593] Subset sums in abelian groups

    22 mars, par (Eric Balandraud), Eric Balandraud
    Denoting by Sigma(S) the set of subset sums of a subset S of a finite abelian group G, we prove that |Sigma(S)| >= |S|(|S|+2)/4-1 whenever S is symmetric, |G| is odd and Sigma(S) is aperiodic. Up to an additive constant of 2 this result is best possible, and we obtain the stronger (exact (...)
  • [hal-02075857] Rudin–Shapiro sequences along squares

    21 mars, par (Christian Mauduit), Christian Mauduit
    We estimate exponential sums of the form Sigma(n <= x) f(n(2)) e(nu n) for a large class of digital functions f and nu is an element of R. We deduce from these estimates the distribution along squares of this class of digital functions which includes the Rudin-Shapiro sequence and some of (...)
  • [hal-02075688] Discrepancy estimates for generalized polynomials

    21 mars, par (Anirban Mukhopadhyay), Anirban Mukhopadhyay
    We obtain an upper bound for the discrepancy of the sequence ([p(n) a] ss) n= 0 generated by the generalized polynomial [p(x) a] ss, where p(x) is a monic polynomial with real coefficients, a and ss are irrational numbers satisfying certain (...)
  • [hal-02075636] Some $q$-supercongruences for truncated basic hypergeometric series

    21 mars, par (Jiang Zeng), Jiang Zeng

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