• Title/Summary/Keyword: twisted L-functions

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ON q-ANALGUE OF THE TWISTED L-FUNCTIONS AND q-TWISTED BERNOULLI NUMBERS

  • Simsek, Yilmaz
    • Journal of the Korean Mathematical Society
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    • v.40 no.6
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    • pp.963-975
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    • 2003
  • The aim of this work is to construct twisted q-L-series which interpolate twisted q-generalized Bernoulli numbers. By using generating function of q-Bernoulli numbers, twisted q-Bernoulli numbers and polynomials are defined. Some properties of this polynomials and numbers are described. The numbers $L_{q}(1-n,\;X,\;{\xi})$ is also given explicitly.

ON A q-ANALOGUE OF THE p-ADIC GENERALIZED TWISTED L-FUNCTIONS AND p-ADIC q-INTEGRALS

  • Lee, Chae-Jang
    • Journal of the Korean Mathematical Society
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    • v.44 no.1
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    • pp.1-10
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    • 2007
  • The purpose of this paper is to define generalized twisted q-Bernoulli numbers by using p-adic q-integrals. Furthermore, we construct a q-analogue of the p-adic generalized twisted L-functions which interpolate generalized twisted q-Bernoulli numbers. This is the generalization of Kim's h-extension of p-adic q-L-function which was constructed in [5] and is a partial answer for the open question which was remained in [3].

MAXIMAL FUNCTIONS ALONG TWISTED SURFACES ON PRODUCT DOMAINS

  • Al-Salman, Ahmad
    • Bulletin of the Korean Mathematical Society
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    • v.58 no.4
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    • pp.1003-1019
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    • 2021
  • In this paper, we introduce a class of maximal functions along twisted surfaces in ℝn×ℝm of the form {(𝜙(|v|)u, 𝜑(|u|)v) : (u, v) ∈ ℝn×ℝm}. We prove Lp bounds when the kernels lie in the space Lq (𝕊n-1×𝕊m-1). As a consequence, we establish the Lp boundedness for such class of operators provided that the kernels are in L log L(𝕊n-1×𝕊m-1) or in the Block spaces B0,0q (𝕊n-1×𝕊m-1) (q > 1).

TWISTED QUADRATIC MOMENTS FOR DIRICHLET L-FUNCTIONS

  • LOUBOUTIN, STEPHANE R.
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.6
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    • pp.2095-2105
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    • 2015
  • Given c, a positive integer, we set. $$M(f,c):=\frac{2}{{\phi}(f)}\sum_{{\chi}{\in}X^-_f}{\chi}(c)|L(1,{\chi})|^2$$, where $X^-_f$ is the set of the $\phi$(f)/2 odd Dirichlet characters mod f > 2, with gcd(f, c) = 1. We point out several mistakes in recently published papers and we give explicit closed formulas for the f's such that their prime divisors are all equal to ${\pm}1$ modulo c. As a Corollary, we obtain closed formulas for M(f, c) for c $\in$ {1, 2, 3, 4, 5, 6, 8, 10}. We also discuss the case of twisted quadratic moments for primitive characters.

Ultrastructure of the Ampullate Gland in the Orb Web Spider, Nephila clavata L. Koch I. Excretory Duct of the Large Ampullate Gland (무당거미(Nephila clavata L. Koch) 병상선(甁狀腺)의 미세구조(微細構造) I. 대병상선(大甁狀腺)의 분비관(分泌管))

  • Moon, Myung-Jin;Kim, Chang-Shik;Kim, Woo-Kap
    • Applied Microscopy
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    • v.18 no.2
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    • pp.77-90
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    • 1988
  • The ultrastructure of the excretory duct of the large ampullate gland in the orb web spider, Nephila clavain L. Koch are studied with light and electron microscopes. The excretory ducts of the large ampullate glands connected with the large spinning tubes(spigots) on the anterior spinnerets are basically composed of three superposed types of the layers which are inner cuticles, monolayered epithelial cells and peripheral connective cells. According to the morphological characteristics of the cuticles and internal textures of the epithelial cells, the long excretory ducts are subdivided into three(distal, middle and proximal) portions. Especially, at the distal portion of the ducts near the spinning tubes, the electron lucent subcuticles which had the functions of water removal and orientation of silk fibers are well distributed, whereas at the middle and proximal portions these layers disappeared and instead of these, endocuticles are developed. The endocuticle contains two types of bands, which are electron dense and electron lucent. And along the length of the cuticular stem in the excretory duct, these two alternating bands are twisted spirally. In the cytoplasm of the columnar epithelial cells of the distal portion, rough endoplasmic reticula and Golgj complexes, related to the production of the cuticular materials are well developed. Between the adjacent epithelial cells, specialized septate junctions and desmosomes are formed along the plasma membranes. At the proximal portion of the duct, densely accumulated secretory materials appeared, and these are released to the inner canal by the apocrine secretion.

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