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  • [hal-00907410] Théorème de Chebotarev effectif

    23 octobre 2017, par Bruno Winckler
    Let K be a number field, and L be a finite normal extension of K with Galois group G. It is known that the number of Frobenius automorphisms corresponding to prime ideals, whose norms are less than x, is equivalent to the logarithmic integral as x tends to infinity, and these automorphisms are (...)
  • [hal-01257924] Very strong approximation for certain algebraic varieties

    23 octobre 2017, par Qing Liu, Fei Xu
    Let F be a global field. In this work, we show that the Brauer-Manin condition on adelic points for subvarieties of a torus T over F cuts out exactly the rational points, if either F is a function field or, if F is the field of rational numbers and T is split. As an application, we prove a (...)
  • [hal-00801781] Surjectivity of Galois representations associated with quadratic Q-curves

    23 octobre 2017, par Samuel Le Fourn
    We prove in this paper an uniform surjectivity result for Galois representations associated with non-CM $\mathbbQ$-curves over imaginary quadratic fields, using various tools for the proof, such as Mazur's method, isogeny theorems, Runge's method and analytic estimates of sums of (...)
  • [hal-01620848] Efficient Optimal Ate Pairing at 128-bit Security Level

    23 octobre 2017, par Md Al-Amin Khandaker, Yuki Nanjo, Loubna Ghammam, Sylvain Duquesne, Yasuyuki Nogami
    Following the emergence of Kim and Barbulescu's new number field sieve (exTNFS) algorithm at CRYPTO'16 [21] for solving discrete logarithm problem (DLP) over the finite field; pairing-based cryptography researchers are intrigued to find new parameters that confirm standard security levels (...)
  • [hal-01620765] Finite beta-expansions with negative bases

    21 octobre 2017, par Zuzana Krčmáriková, Wolfgang Steiner, Tomáš Vávra
    The finiteness property is an important arithmetical property of beta-expansions. We exhibit classes of Pisot numbers $\beta$ having the negative finiteness property, that is the set of finite $(-\beta)$-expansions is equal to $\mathbbZ[\beta^-1]$. For a class of numbers including the (...)

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