Mostrando recursos 1 - 20 de 55

  1. A note on transcendental entire functions mapping uncountable many Liouville numbers into the set of Liouville numbers

    Lelis, Jean; Marques, Diego; Ramirez, Josimar
    In 1906, Maillet proved that given a non-constant rational function $f$, with rational coefficients, if $\xi$ is a Liouville number, then so is $f(\xi)$. Motivated by this fact, in 1984, Mahler raised the question about the existence of transcendental entire functions with this property. In this work, we define an uncountable subset of Liouville numbers for which there exists a transcendental entire function taking this set into the set of the Liouville numbers.

  2. An explicit formula of the unramified Shintani functions for $(\mathbf{GSp}_{4},\mathbf{GL}_{2} \times_{\mathbf{GL}_{1}} \mathbf{GL}_{2})$ and its application

    Gejima, Kohta
    Let $F$ be a non-archimedean local field of arbitrary characteristic. In this paper, we announce an explicit formula of the unramified Shintani functions for $(\mathbf{GSp}_{4}(F),(\mathbf{GL}_{2} \times_{\mathbf{GL}_{1}} \mathbf{GL}_{2})(F))$. As an application, we compute a local zeta integral, which represents the spin $L$-factor of $\mathbf{GSp}_{4}$.

  3. Semi-discrete finite difference schemes for the nonlinear Cauchy problems of the normal form

    Higashimori, Nobuyuki; Fujiwara, Hiroshi
    We consider the Cauchy problems of nonlinear partial differential equations of the normal form in the class of analytic functions. We apply semi-discrete finite difference approximation which discretizes the problems only with respect to the time variable, and we give a proof for its convergence. The result implies that there are cases of convergence of finite difference schemes applied to ill-posed Cauchy problems.

  4. Examples of genus two fibrations with no sections on rational surfaces

    Kitagawa, Shinya
    We construct explicit examples of genus two fibrations with no sections on rational surfaces by the double covering method. For the proof of non-existence of sections, we use the theory of the virtual Mordell-Weil groups.

  5. Symmetry breaking operators for the restriction of representations of indefinite orthogonal groups $O(p,q)$

    Kobayashi, Toshiyuki; Leontiev, Alex
    For the pair $(G, G') =(O(p+1, q+1), O(p,q+1))$, we construct and give a complete classification of intertwining operators (\textit{symmetry breaking operators}) between most degenerate spherical principal series representations of $G$ and those of the subgroup $G'$, extending the work initiated by Kobayashi and Speh [Mem. Amer. Math. Soc. 2015] in the real rank one case where $q=0$. Functional identities and residue formul{æ} of the regular symmetry breaking operators are also provided explicitly. The results contribute to Program C of branching problems suggested by the first author [Progr. Math. 2015].

  6. Symmetry breaking operators for the restriction of representations of indefinite orthogonal groups $O(p,q)$

    Kobayashi, Toshiyuki; Leontiev, Alex
    For the pair $(G, G') =(O(p+1, q+1), O(p,q+1))$, we construct and give a complete classification of intertwining operators (symmetry breaking operators) between most degenerate spherical principal series representations of $G$ and those of the subgroup $G'$, extending the work initiated by Kobayashi and Speh [Mem. Amer. Math. Soc. 2015] in the real rank one case where $q=0$. Functional identities and residue formulæ of the regular symmetry breaking operators are also provided explicitly. The results contribute to Program C of branching problems suggested by the first author [Progr. Math. 2015].

  7. An algebraic proof of determinant formulas of Grothendieck polynomials

    Matsumura, Tomoo
    We give an algebraic proof of the determinant formulas for factorial Grothendieck polynomials obtained by Hudson–Ikeda–Matsumura–Naruse in~[6] and by Hudson–Matsumura in~[7].

  8. An algebraic proof of determinant formulas of Grothendieck polynomials

    Matsumura, Tomoo
    We give an algebraic proof of the determinant formulas for factorial Grothendieck polynomials obtained by Hudson–Ikeda–Matsumura–Naruse in [6] and by Hudson–Matsumura in [7].

  9. A character of the Siegel modular group of level 2 from theta constants

    Xiong, Xinhua
    Given a characteristic, we define a character of the Siegel modular group of level 2, the computations of their values are obtained. Using our theorems, some key theorems of Igusa~[2] can be recovered.

  10. A character of the Siegel modular group of level 2 from theta constants

    Xiong, Xinhua
    Given a characteristic, we define a character of the Siegel modular group of level 2, the computations of their values are obtained. Using our theorems, some key theorems of Igusa [2] can be recovered.

  11. Semicomplete vector fields on non-Kähler surfaces

    Guillot, Adolfo
    We investigate semicomplete meromorphic vector fields on complex surfaces, those where the solutions of the associated ordinary differential equations have no multivaluedness. We prove that if a non-Kähler compact complex surface has such a vector field, then, up to a bimeromorphic transformation, either the vector field is holomorphic, has a first integral or preserves a fibration. This extends previous results of Rebelo and the author to the non-Kähler setting.

  12. Semicomplete vector fields on non-Kähler surfaces

    Guillot, Adolfo
    We investigate semicomplete meromorphic vector fields on complex surfaces, those where the solutions of the associated ordinary differential equations have no multivaluedness. We prove that if a non-Kähler compact complex surface has such a vector field, then, up to a bimeromorphic transformation, either the vector field is holomorphic, has a first integral or preserves a fibration. This extends previous results of Rebelo and the author to the non-Kähler setting.

  13. Corrigendum On the class groups of pure function fields

    Ichimura, Humio

  14. Corrigendum On the class groups of pure function fields

    Ichimura, Humio

  15. A note on the Rankin-Selberg method for Siegel cusp forms of genus 2

    Horie, Taro

  16. A note on the Rankin-Selberg method for Siegel cusp forms of genus 2

    Horie, Taro

  17. A Thermodynamic formalism for one dimensional cellular automata

    Namiki, Takao

  18. A Thermodynamic formalism for one dimensional cellular automata

    Namiki, Takao

  19. The Bergman kernel on weakly pseudoconvex tube domains in $\mathbf {C}^2$

    Kamimoto, Joe

  20. The Bergman kernel on weakly pseudoconvex tube domains in $\mathbf {C}^2$

    Kamimoto, Joe

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