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  • [hal-00868107] A Structure result for bricks in Heisenberg groups

    16 octobre 2017, par Norbert Hegyvári, François Hennecart
    We show that for a sufficiently big \textitbrick $B$ of the $(2n+1)$-dimensional Heisenberg group $H_n$ over the finite field $\mathbbF_p$, the product set $B\cdot B$ contains at least $|B|/p$ many cosets of some non trivial subgroup of (...)
  • [hal-00867368] Distribution of residues in approximate subgroups of $\mathbb{F}_p^*$

    16 octobre 2017, par Norbert Hegyvári, Francois Hennecart
    We extend a result due to Bourgain on the uniform distribution of residues by proving that subsets of the type $f(I)\cdot H$ is equidistributed (as $p$ tends to infinity) where $f$ is a polynomial, $I$ is an interval of $\Fp$ and $H$ is an approximate subgroup of $\mathbbF_p^*$ with size larger (...)
  • [hal-01053353] q-Ehrhart polynomials of Gorenstein polytopes,\\Bernoulli umbra and related Dirichlet series

    16 octobre 2017, par Frédéric Chapoton, Driss Essouabri
    This article considers some q-analogues of classical results concerning the Ehrhart polynomials of Gorenstein polytopes, namely properties of their q-Ehrhart polynomial with respect to a good linear form. Another theme is a specific linear form Ψ (involving Carlitz' q-analogues of Bernoulli (...)
  • [hal-01287140] Algebraic independence of $G$-functions and congruences "à la Lucas".

    16 octobre 2017, par B Adamczewski, Jason P. Bell, E Delaygue
    We develop a new method for proving algebraic independence of $G$-functions. Our approach rests on the following observation: $G$-functions do not always come with a single linear differential equation, but also sometimes with an infinite family of linear difference equations associated with (...)
  • [hal-00666154] Small values of the Euler function and the Riemann hypothesis

    16 octobre 2017, par Jean-Louis Nicolas
    Let $\vfi$ be Euler's function, $\ga$ be Euler's constant and $N_k$ be the product of the first $k$ primes. In this article, we consider the function $c(n) =(n/\vfi(n)-e^\ga\log\log n)\sqrt\log n$. Under Riemann's hypothesis, it is proved that $c(N_k)$ is bounded and explicit bounds are given (...)

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