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  • [hal-01625653] A conjecture which implies that there are infinitely many primes of the form n !+1

    31 octobre 2017, par Apoloniusz Tyszka
    Let f(6)=720, and let f(n+1)=f(n)! for every integer n \geq 6. For an integer n \geq 6, let \Lambda_n denote the following statement: if a system S \subseteq x_i!=x_j: 1 \leq i < j \leq n \cup x_i \cdot x_j=x_j+1: 1 \leq i < j \leq n-1 has at most finitely many solutions in integers (...)
  • [hal-01626429] Julia Robinson’s Numbers

    31 octobre 2017, par Pierre Gillibert, Gabriele Ranieri
    We partially answer to a question of Vidaux and Videla by constructing an infinite family of rings of algebraic integers of totally real subfields of Q whose Julia Robinson's Number is distinct from 4 and +∞. Moreover the set of the Julia Robinson's Number that we construct is (...)
  • [hal-01161783] Decoding of Repeated-Root Cyclic Codes up to New Bounds on Their Minimum Distance

    27 octobre 2017, par Alexander Zeh, Markus Ulmschneider
    The well-known approach of Bose, Ray-Chaudhuri and Hocquenghem and its generalization by Hartmann and Tzeng are lower bounds on the minimum distance of simple-root cyclic codes. We generalize these two bounds to the case of repeated-root cyclic codes and present a syndrome-based burst error (...)
  • [hal-01625166] On the Explicit Torsion Anomalous Conjecture

    27 octobre 2017, par Sara Checcoli, Francesco Veneziano, Evelina Viada
    The Torsion Anomalous Conjecture states that an irreducible variety $V$ embedded in a semi-abelian variety contains only finitely many maximal $V$-torsion anomalous varieties. In this paper we consider an irreducible variety embedded in a product of elliptic curves. Our main result provides a (...)
  • [hal-01625161] On torsion anomalous intersections

    27 octobre 2017, par Sara Checcoli, Francesco Veneziano, Evelina Viada
    A deep conjecture on torsion anomalous varieties states that if $V$ is a weak-transverse variety in an abelian variety, then the complement $V^ta$ of all $V$-torsion anomalous varieties is open and dense in $V$. We prove some cases of this conjecture. We show that the $V$-torsion anomalous (...)

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