Mostrando recursos 1 - 20 de 78

  1. Analytic continuation of the multiple Fibonacci zeta functions

    Rout, Sudhansu Sekhar; Meher, Nabin Kumar
    In this article, we prove the meromorphic continuation of the multiple Fibonacci zeta functions of depth 2: \begin{equation*} \sum_{0 0$ and $\mathop{\mathrm{Re}} (s_{2}) > 0$. We compute a complete list of its poles and their residues. We also prove that multiple Fibonacci zeta values at negative integer arguments are rational.

  2. Automorphism group of plane curve computed by Galois points, II

    Harui, Takeshi; Miura, Kei; Ohbuchi, Akira
    Recently, the first author~[3] classified finite groups obtained as automorphism groups of smooth plane curves of degree $d \ge 4$ into five types. He gave an upper bound of the order of the automorphism group for each types. For one of them, the type (a-ii), that is given by $\max \{2d (d - 2), 60 d\}$. In this article, we shall construct typical examples of smooth plane curve $C$ by applying the method of Galois points, whose automorphism group has order $60d$. In fact, we determine the structure of the automorphism group of those curves.

  3. A note on the dimension of global sections of adjoint bundles for polarized 4-folds

    Fukuma, Yoshiaki
    Let $(X,L)$ be a polarized manifold defined over the field of complex numbers. In this paper, we consider the case where $\dim X=4$ and we prove that the second Hilbert coefficient $A_{2}(X,L)$ of $(X,L)$, which was defined in our previous paper, is non-negative. Furthermore we consider a question proposed by H. Tsuji for $\dim X=4$.

  4. Non-left-orderable surgeries on negatively twisted torus knots

    Ichihara, Kazuhiro; Temma, Yuki
    We show that certain negatively twisted torus knots admit Dehn surgeries yielding 3-manifolds with non-left-orderable fundamental groups.

  5. On a Galois group arising from an iterated map

    Shimakura, Masamitsu
    We study the irreducibility and the Galois group of the polynomial $f (a,x) = x^{8} +3ax^{6}+3a^{2}x^{4}+(a^{2}+1)ax^{2}+a^{2}+1$ over $\mathbf{Q}(a)$ and $\mathbf{Q}$. This polynomial is a factor of the 4-th dynatomic polynomial for the map $\sigma(x) = x^{3} + ax$.

  6. Inequalities for free multi-braid arrangements

    DiPasquale, Michael Robert
    Abe, Nuida, and Numata (2009) describe a large class of free multiplicities on the braid arrangement arising from signed-eliminable graphs. On a large cone in the multiplicity lattice, we prove that these are the only free multiplicities on the braid arrangement. We also give a conjecture on the structure of all free multiplicities on the braid arrangement.

  7. Self-similar measures for iterated function systems driven by weak contractions

    Okamura, Kazuki
    We show the existence and uniqueness for self-similar measures for iterated function systems driven by weak contractions. Our main idea is using the duality theorem of Kantorovich-Rubinstein and equivalent conditions for weak contractions established by Jachymski. We also show collage theorems for such iterated function systems.

  8. Complete flat fronts as hypersurfaces in Euclidean space

    Honda, Atsufumi
    By Hartman–Nirenberg’s theorem, any complete flat hypersurface in Euclidean space muast be a cylinder over a plane curve. However, if we admit some singularities, there are many non-trivial examples. {\it Flat fronts} are flat hypersurfaces with admissible singularities. Murata–Umehara gave a representation formula for complete flat fronts with non-empty singular set in Euclidean 3-space, and proved the four vertex type theorem. In this paper, we prove that, unlike the case of $n=2$, there do not exist any complete flat fronts with non-empty singular set in Euclidean $(n+1)$-space $(n\geq 3)$.

  9. On Koyama’s refinement of the prime geodesic theorem

    Avdispahić, Muharem
    We give a new proof of the best presently-known error term in the prime geodesic theorem for compact hyperbolic surfaces, without the assumption of excluding a set of finite logarithmic measure. Stronger implications of the Gallagher-Koyama approach are derived, yielding to a further reduction of the error term outside a set of finite logarithmic measure.

  10. Rational quotients of two linear forms in roots of a polynomial

    Dubickas, Artūras
    Let $f$ and $g$ be two linear forms with non-zero rational coefficients in $k$ and $\ell$ variables, respectively. We describe all separable polynomials $P$ with the property that for any choice of (not necessarily distinct) roots $\lambda_{1},\ldots,\lambda_{k+\ell}$ of $P$ the quotient between $f(\lambda_{1},\ldots,\lambda_{k})$ and $g(\lambda_{k+1},\ldots,\lambda_{k+\ell}) \ne 0$ belongs to $\mathbf{Q}$. It turns out that each such polynomial has all of its roots in a quadratic extension of $\mathbf{Q}$. This is a continuation of a recent work of Luca who considered the case when $k=\ell=2$, $f(x_{1},x_{2})$ and $g(x_{1},x_{2})$ are both $x_{1}-x_{2}$, solved it, and raised the above problem as an open...

  11. A $p$-analogue of Euler’s constant and congruence zeta functions

    Kurokawa, Nobushige; Taguchi, Yuichiro
    A $p$-analogue of a formula of Euler on the Euler constant is given, and it is interpreted in terms of the absolute zeta functions of tori.

  12. SVV algebras

    Walker, Ruari Donald
    In 2010 Shan, Varagnolo and Vasserot introduced a family of graded algebras in order to prove a conjecture of Kashiwara and Miemietz which stated that the finite-dimensional representations of affine Hecke algebras of type $D$ categorify a module over a certain quantum group. We study these algebras, and in various cases, show how they relate to Varagnolo-Vasserot algebras and to quiver Hecke algebras which in turn allows us to deduce various homological properties.

  13. The local zeta integrals for $\mathit{GL}(2,\mathbf{C})\times \mathit{GL}(2,\mathbf{C})$

    Miyazaki, Tadashi
    In this article, for irreducible admissible infinite-dimensional representations $\Pi$ and $\Pi'$ of $\mathit{GL}(2,\mathbf{C})$, we show that the local $L$-factor $L(s,\Pi \times \Pi')$ can be expressed as some local zeta integral for $\mathit{GL}(2,\mathbf{C})\times \mathit{GL}(2,\mathbf{C})$.

  14. Graded Lie algebras and regular prehomogeneous vector spaces with one-dimensional scalar multiplication

    Sasano, Nagatoshi
    The aim of this paper is to study relations between regular reductive prehomogeneous vector spaces (PVs) with one-dimensional scalar multiplication and the structure of graded Lie algebras. We will show that the regularity of such PVs is described by an $\mathfrak{sl}_{2}$-triplet of a graded Lie algebra.

  15. Applications of the Laurent-Stieltjes constants for Dirichlet $L$-series

    Saad Eddin, Sumaia
    The Laurent-Stieltjes constants $\gamma_{n}(\chi)$ are, up to a trivial coefficient, the coefficients of the Laurent expansion of the usual Dirichlet $L$-series: when $\chi$ is non-principal, $(-1)^{n}\gamma_{n}(\chi)$ is simply the value of the $n$-th derivative of $L(s,\chi)$ at $s=1$. In this paper, we give an approximation of the Dirichlet $L$-functions in the neighborhood of $s=1$ by a short Taylor polynomial. We also prove that the Riemann zeta function $\zeta(s)$ has no zeros in the region $|s-1|\leq 2.2093$, with $0\leq \Re{(s)}\leq 1$. This work is a continuation of [24].

  16. Some remarks on log surfaces

    Liu, Haidong
    Fujino and Tanaka established the minimal model theory for $\mathbf{Q}$-factorial log surfaces in characteristic 0 and $p$, respectively. We prove that every intermediate surface has only log terminal singularities if we run the minimal model program starting with a pair consisting of a smooth surface and a boundary $\mathbf{R}$-divisor. We further show that such a property does not hold if the initial surface is singular.

  17. 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.

  18. 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 $\mathbf{GSp}_{4}$.

  19. 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.

  20. 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.

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