• Title/Summary/Keyword: Meromorphic

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Semigroups which are not weierstrass semigroups

  • Kim, Seon-Jeong
    • Bulletin of the Korean Mathematical Society
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    • v.33 no.2
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    • pp.187-191
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    • 1996
  • Let C be a nonsingular complex projective algebraic curve (or a compact Riemann surface) of genus g. Let $M(C)$ denote the field of meromorphic functions on C and N the set of all non-negative integers.

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EISENSTEIN SERIES WITH NON-UNITARY TWISTS

  • Deitmar, Anton;Monheim, Frank
    • Journal of the Korean Mathematical Society
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    • v.55 no.3
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    • pp.507-530
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    • 2018
  • It is shown that for a non-unitary twist of a Fuchsian group, which is unitary at the cusps, Eisenstein series converge in some half-plane. It is shown that invariant integral operators provide a spectral decomposition of the space of cusp forms and that Eisenstein series admit a meromorphic continuation.

Weighted Value Sharing and Uniqueness of Entire Functions

  • Sahoo, Pulak
    • Kyungpook Mathematical Journal
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    • v.51 no.2
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    • pp.145-164
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    • 2011
  • In the paper, we study with weighted sharing method the uniqueness of entire functions concerning nonlinear differential polynomials sharing one value and prove two uniqueness theorems, first one of which generalizes some recent results in [10] and [16]. Our second theorem will supplement a result in [17].

SOME RESULTS RELATED TO DIFFERENTIAL-DIFFERENCE COUNTERPART OF THE BRÜCK CONJECTURE

  • Md. Adud;Bikash Chakraborty
    • Communications of the Korean Mathematical Society
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    • v.39 no.1
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    • pp.117-125
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    • 2024
  • In this paper, our focus is on exploring value sharing problems related to a transcendental entire function f and its associated differential-difference polynomials. We aim to establish some results which are related to differential-difference counterpart of the Brück conjecture.

A RESULT ON AN OPEN PROBLEM OF LÜ, LI AND YANG

  • Majumder, Sujoy;Saha, Somnath
    • Bulletin of the Korean Mathematical Society
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    • v.58 no.4
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    • pp.915-937
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    • 2021
  • In this paper we deal with the open problem posed by Lü, Li and Yang [10]. In fact, we prove the following result: Let f(z) be a transcendental meromorphic function of finite order having finitely many poles, c1, c2, …, cn ∈ ℂ\{0} and k, n ∈ ℕ. Suppose fn(z), f(z+c1)f(z+c2) ⋯ f(z+cn) share 0 CM and fn(z)-Q1(z), (f(z+c1)f(z+c2) ⋯ f(z+cn))(k) - Q2(z) share (0, 1), where Q1(z) and Q2(z) are non-zero polynomials. If n ≥ k+1, then $(f(z+c_1)f(z+c_2)\;{\cdots}\;f(z+c_n))^{(k)}\;{\equiv}\;{\frac{Q_2(z)}{Q_1(z)}}f^n(z)$. Furthermore, if Q1(z) ≡ Q2(z), then $f(z)=c\;e^{\frac{\lambda}{n}z}$, where c, λ ∈ ℂ \ {0} such that eλ(c1+c2+⋯+cn) = 1 and λk = 1. Also we exhibit some examples to show that the conditions of our result are the best possible.

On the Growth of Transcendental Meromorphic Solutions of Certain algebraic Difference Equations

  • Xinjun Yao;Yong Liu;Chaofeng Gao
    • Kyungpook Mathematical Journal
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    • v.64 no.1
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    • pp.185-196
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    • 2024
  • In this article, we investigate the growth of meromorphic solutions of $${\alpha}(z)(\frac{{\Delta}_c{\eta}}{{\eta}})^2\,+\,(b_2(z){\eta}^2(z)\;+\;b_1(z){\eta}(z)\;+\;b_0(z))\frac{{\Delta}_c{\eta}}{{\eta}} \atop =d_4(z){\eta}^4(z)\;+\;d_3(z){\eta}^3(z)\;+\;d_2(z){\eta}^2(z)\;+\;d_1(z){\eta}(z)\;+\;d_0(z),$$ where a(z), bi(z) for i = 0, 1, 2 and dj (z) for j = 0, ..., 4 are given functions, △cη = η(z + c) - η(z) with c ∈ ℂ\{0}. In particular, when the a(z), the bi(z) and the dj(z) are polynomials, and d4(z) ≡ 0, we shall show that if η(z) is a transcendental entire solution of finite order, and either deg a(z) ≠ deg d0(z) + 1, or, deg a(z) = deg d0(z) + 1 and ρ(η) ≠ ½, then ρ(η) ≥ 1.