Mostrando recursos 1 - 20 de 6.539

  1. Value distribution of L-functions concerning shared values and certain differential polynomials

    Liu, Fang; Li, Xiao-Min; Yi, Hong-Xun
    In this paper, we study a uniqueness question of meromorphic functions of certain differential polynomials that share a nonzero finite value or have the same fixed points with the same of L-functions. The results in this paper extend the corresponding results from Steuding \cite[p.~152]{rf12}, Li~[7], Fang~[1] and Yang-Hua~[14].

  2. On the distribution of rank two $\tau$-congruent numbers

    Davis, Chad Tyler
    A positive integer $n$ is the area of a Heron triangle if and only if there is a non-zero rational number $\tau$ such that the elliptic curve \begin{equation*} E_{τ}^{(n)}: Y^{2} = X(X-nτ)(X+nτ^{-1}) \end{equation*} has a rational point of order different than two. Such integers $n$ are called $\tau$-congruent numbers. In this paper, we show that for a given positive integer $p$, and a given non-zero rational number $\tau$, there exist infinitely many $\tau$-congruent numbers in every residue class modulo $p$ whose corresponding elliptic curves have rank at least two.

  3. On the product of Hurwitz zeta-functions

    Wang, Nian Liang; Banerjee, Soumyarup
    Corresponding to the lattice point problem for a random sphere Kendall and Rankin~[8], Nakajima~[9] considered the summatory function of the coefficients of the product of two Hurwitz zeta-functions and obtained the Bessel series expression. In this note we treat the case of the product of $\varkappa$ Hurwitz zeta-functions for an arbitrary integer $\varkappa\ge 2$ and obtain the expression in terms of the Voronoï-Steen function. This amounts to a refinement of corrected Nakajima’s formula with streamlining of the ambiguous argument.

  4. Escape rate of the Brownian motions on hyperbolic spaces

    Shiozawa, Yuichi
    We discuss the escape rate of the Brownian motion on a hyperbolic space. We point out that the escape rate is determined by using the Brownian expression of the radial part and a generalized Kolmogorov’s test for the one dimensional Brownian motion.

  5. Evans-Selberg potential on planar domains

    Dong, Robert Xin
    We provide explicit formulas of Evans kernels, Evans-Selberg potentials and fundamental metrics on potential-theoretically parabolic planar domains.

  6. On the Letac-Massam Conjecture on cones $Q_{A_{n}}$

    Graczyk, Piotr; Ishi, Hideyuki; Mamane, Salha; Ochiai, Hiroyuki
    We prove, for graphical models for nearest neighbour interactions, a conjecture stated by Letac and Massam in 2007. Our result is important in the analysis of Wishart distributions on cones related to graphical models and in its statistical applications.

  7. Telescopic approach to a formula of ${_{2}}F_{1}$-series by Gosper and Ebisu

    Chu, Wenchang
    By means of the telescoping method, we prove an infinite series identity with four free parameters. Its limiting case is utilized, with the help of the Pfaff transformation, not only to present a new proof for a ${_{2}}F_{1}$-series identity conjectured by Gosper (1977) and proved recently by Ebisu (2013), but also to establish an extension of the binomial series.

  8. Borel structures coming from various topologies on $\mathbf{B}(\mathcal{H})$

    Bagheri-Bardi, Ghorban Ali; Khosheghbal-Ghorabayi, Minoo
    Although there exist different types of (well-known) locally convex topologies on $\mathbf{B}(\mathcal{H})$, the notion of measurability on the set of operator valued functions $f:\Omega\to \mathbf{B}(\mathcal{H})$ is unique when $\mathcal{H}$ is separable (see~[1]). In this current discussion we observe that unlike the separable case, in the non-separable case we have to face different types of measurability. Moreover the algebraic operations “\textit{addition and product}” are not compatible with the set of operator valued measurable functions.

  9. Borel structures coming from various topologies on $\mathbf{B}(\mathcal{H})$

    Bagheri-Bardi, Ghorban Ali; Khosheghbal-Ghorabayi, Minoo
    Although there exist different types of (well-known) locally convex topologies on $\mathbf{B}(\mathcal{H})$, the notion of measurability on the set of operator valued functions $f:\Omega\to \mathbf{B}(\mathcal{H})$ is unique when $\mathcal{H}$ is separable (see [1]). In this current discussion we observe that unlike the separable case, in the non-separable case we have to face different types of measurability. Moreover the algebraic operations “addition and product” are not compatible with the set of operator valued measurable functions.

  10. Quasi-symmetries and rigidity for determinantal point processes associated with de Branges spaces

    Bufetov, Alexander Igorevich; Shirai, Tomoyuki
    In this note, we show that determinantal point processes on the real line corresponding to de Branges spaces of entire functions are rigid in the sense of Ghosh-Peres and, under certain additional assumptions, quasi-invariant under the group of diffeomorphisms of the line with compact support.

  11. Note on a general complex Monge-Ampère equation on pseudoconvex domains of infinite type

    Ha, Ly Kim
    Let $\Omega$ be a smoothly bounded domain in $\mathbf{C}^{n}$, for $n\ge 2$. For a given continuous function $\phi$ on $b\Omega$, and a non-negative continuous function $\Psi$ on $\mathbf{R}\times \overline{\Omega}$, the main purpose of this note is to seek a plurisubharmonic function $u$ on $\Omega$, continuous on $\overline{\Omega}$, which solves the following Dirichlet problem of the complex Monge-Ampère equation \begin{equation*} \begin{cases} \det\left[\dfrac{\partial^{2}(u)}{\partial z_{i}\partial\bar{z}_{j}}\right](z)=\Psi(u(z),z)\geqslant 0 & \text{in}\quad\Omega,\\ u=\phi & \text{on}\quad b\Omega. \end{cases} \end{equation*} In particular, the boundary regularity for the solution of this complex, fully nonlinear equation is studied when $\Omega$ belongs to a large class of weakly pseudoconvex domains of finite and infinite type in $\mathbf{C}^{n}$.

  12. On ergodic measures with negative Lyapunov exponents

    Barragán, Andrés Mauricio; Morales, Carlos Arnoldo
    We prove for $n\geq 3$ that every nonatomic ergodic measure of an $n$-dimensional flow whose Lyapunov exponents off the flow direction are all negative is supported on an attracting periodic orbit.

  13. Hardy’s inequality on Hardy spaces

    Ho, Kwok-Pun
    We extend the Hardy inequalities to the classical Hardy spaces and the rearrangement-invariant Hardy spaces.

  14. Toric 2-Fano manifolds and extremal contractions

    Sato, Hiroshi
    We show that for a projective toric manifold with the ample second Chern character, if there exists a Fano contraction, then it is isomorphic to the projective space. For the case that the second Chern character is nef, the Fano contraction gives either a projective line bundle structure or a direct product structure. We also show that, for a toric weakly 2-Fano manifold, there does not exist a divisorial contraction to a point.

  15. A positivity conjecture related first positive rank and crank moments for overpartitions

    Xiong, Xinhua
    Recently, Andrews, Chan, Kim and Osburn introduced a $q$-series $h(q)$ for the study of the first positive rank and crank moments for overpartitions. They conjectured that for all integers $m \geq 3$, \begin{equation*} \frac{1}{(q)_{∞}} (h(q) - m h(q^{m})) \end{equation*} has positive power series coefficients for all powers of $q$. Byungchan Kim, Eunmi Kim and Jeehyeon Seo provided a combinatorial interpretation and proved it is asymptotically true. In this note, we show this conjecture is true if $m$ is any positive power of 2, and we show that in order to prove this conjecture, it is only to prove it for all primes $m$. Moreover...

  16. Balancing non-Wieferich primes in arithmetic progression and $abc$ conjecture

    Rout, Sudhansu Sekhar
    In this note, we shall define the balancing Wieferich prime which is an analogue of the famous Wieferich primes. We prove that, under the $abc$ conjecture for the number field $\mathbf{Q}(\sqrt{2})$, there are infinitely many balancing non-Wieferich primes. In particular, under the assumption of the $abc$ conjecture for the number field $\mathbf{Q}(\sqrt{2})$ there are at least $O(\log x/{\log \log x})$ such primes $p \equiv 1(\mathrm{mod}\ k)$ for any fixed integer $k> 2$.

  17. Ruelle zeta functions for finite dynamical systems and Koyama-Nakajima’s $L$-functions

    Hattori, Yukihiro; Morita, Hideaki
    A complex reflection determines an $L$-function which is a generalization of the Artin-Mazur zeta function associated with an element of the symmetric group. The present paper shows that the $L$-function is the Ruelle zeta function associated with a weighted $\mathbf{Z}$-dynamical system.

  18. Remarks on the abundance conjecture

    Hashizume, Kenta
    We prove the abundance theorem for log canonical $n$-folds such that the boundary divisor is big assuming the abundance conjecture for log canonical $(n-1)$-folds. We also discuss the log minimal model program for log canonical 4-folds.

  19. The representation function for sums of three squares along arithmetic progressions

    Pollack, Paul
    For positive integers $n$, let $r(n) = \#\{(x,y,z) \in\mathbf{Z}^{3}: x^{2}+y^{2}+z^{2}=n\}$. Let $g$ be a positive integer, and let $A\bmod{M}$ be any congruence class containing a squarefree integer. We show that there are infinitely many squarefree positive integers $n\equiv A\bmod{M}$ for which $g$ divides $r(n)$. This generalizes a result of Cho.

  20. Resurgence of formal series solutions of nonlinear differential and difference equations

    Kamimoto, Shingo
    We discuss the resurgence of formal series solutions of nonlinear differential and difference equations of level 1. We derive an estimate for iterated convolution products. We describe the possible location of the singularities of their Borel transforms.

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