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  • [hal-01571121] On special values of standard L-functions of Siegel cusp eigenforms of genus 3

    1er août, par Anh Tuan Do, Kirill Vankov
    We explicitly compute the special values of the standard $L$-function $L(s, F_12, \mathrmSt)$ at the critical points $s\in \lbrace -8, -6, -4, -2, 0, 1, 3, 5, 7, 9\rbrace $, where $F_12$ is the unique (up to a scalar) Siegel cusp form of degree $3$ and weight $12$, which was constructed by (...)
  • [hal-01571117] Explicit Hecke series for symplectic group of genus 4

    1er août, par Kirill Vankov
    Shimura conjectured the rationality of the generating series for Hecke operators for the symplectic group of genus $n$. This conjecture was proved by Andrianov for arbitrary genus $n$, but the explicit expression was out of reach for genus higher than 3. For genus $n=4$, we explicitly compute (...)
  • [hal-01571090] Spherical Image of Local Hecke Series of Genus Four

    1er août, par Kirill Vankov
    Получена явная формула образа при сферическом отображении дроби многочленов, предложенная Шимурой в 1963 г. для производящих рядов Гекке рода 4. Для вычислений мы использовали формулы Андрианова для сферического отображения Сатаке, которые подробно описаны в нашей предыдущей (...)
  • [hal-01571086] Spherical image of local Hecke series of genus four

    1er août, par Kirill Vankov
    For the spherical image of a polynomial fraction, we obtain the explicit formula conjectured by Shimura in 1963 for generating Hecke series in the particular case of genus 4. As in our previous work, we use formulas due to Andrianov for the Satake spherical (...)
  • [hal-01571077] Explicit Shimura’s conjecture for Sp3 on a computer

    1er août, par Kirill Vankov, Alexei Pantchichkine
    We compute by a different method the generating series in Shimura's conjecture for Sp3, proved by Andrianov in 1967. We develop formulas for the Satake spherical maps for Spn and GLn.

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