• Title/Summary/Keyword: p-adic integrals

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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].

GREEN FUNCTIONS ON THE p-ADIC VECTOR SPACE

  • SON, JIN-Woo;RIM, KYUNG-SOO
    • Communications of the Korean Mathematical Society
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    • v.20 no.4
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    • pp.657-669
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    • 2005
  • Calculations of some integrals on the n-dimensional vector space over $\mathbb{Q}_p$ are useful in getting some other formulations of quantum mechanics and the field theory of p-adic mathematical physics. For reasons of these, we estimate several integrals. As an application, we derive some properties for the p-adic Green functions.

SOME IDENTITIES OF DEGENERATE GENOCCHI POLYNOMIALS

  • Lim, Dongkyu
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.2
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    • pp.569-579
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    • 2016
  • L. Carlitz introduced higher order degenerate Euler polynomials in [4, 5] and studied a degenerate Staudt-Clausen theorem in [4]. D. S. Kim and T. Kim gave some formulas and identities of degenerate Euler polynomials which are derived from the fermionic p-adic integrals on ${\mathbb{Z}}_p$ (see [9]). In this paper, we introduce higher order degenerate Genocchi polynomials. And we give some formulas and identities of degenerate Genocchi polynomials which are derived from the fermionic p-adic integrals on ${\mathbb{Z}}_p$.

ON THE q-EXTENSION OF THE HARDY-LITTLEWOOD-TYPE MAXIMAL OPERATOR RELATED TO q-VOLKENBORN INTEGRAL IN THE p-ADIC INTEGER RING

  • Jang, Lee-Chae
    • Journal of the Chungcheong Mathematical Society
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    • v.23 no.2
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    • pp.207-213
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    • 2010
  • In this paper, we define the q-extension of the Hardy-Littlewood-type maximal operator related to q-Volkenborn integral. By the meaning of the extension of q-Volkenborn integral, we obtain the boundedness of the q-extension of the Hardy-Littlewood-type maximal operator in the p-adic integer ring.

ON BERNOULLI NUMBERS

  • Kim, Min-Soo;Son, Jin-Woo
    • Journal of the Korean Mathematical Society
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    • v.37 no.3
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    • pp.391-410
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    • 2000
  • In the complex case, we construct a q-analogue of the Riemann zeta function q(s) and a q-analogue of the Dirichlet L-function L(s,X), which interpolate the 1-analogue Bernoulli numbers. Using the properties of p-adic integrals and measures, we show that Kummer type congruences for the q-analogue Bernoulli numbers are the generalizations of the usual Kummer congruences for the ordinary Bernoulli numbers. We also construct a q0analogue of the p-adic L-function Lp(s, X;q) which interpolates the q-analogue Bernoulli numbers at non positive integers.

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DEGENERATE BERNOULLI NUMBERS AND POLYNOMIALS ASSOCIATED WITH DEGENERATE HERMITE POLYNOMIALS

  • Haroon, Hiba;Khan, Waseem Ahmad
    • Communications of the Korean Mathematical Society
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    • v.33 no.2
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    • pp.651-669
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    • 2018
  • The article is themed to classify new (fully) degenerate Hermite-Bernoulli polynomials with formulation in terms of p-adic fermionic integrals on $\mathbb{Z}_p$. The entire paper is designed to illustrate new properties in association with Daehee polynomials in a consolidated and generalized form.

SOME SYMMETRY IDENTITIES FOR GENERALIZED TWISTED BERNOULLI POLYNOMIALS TWISTED BY UNRAMIFIED ROOTS OF UNITY

  • Kim, Dae San
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.2
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    • pp.603-618
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    • 2015
  • We derive three identities of symmetry in two variables and eight in three variables related to generalized twisted Bernoulli polynomials and generalized twisted power sums, both of which are twisted by unramified roots of unity. The case of ramified roots of unity was treated previously. The derivations of identities are based on the p-adic integral expression, with respect to a measure introduced by Koblitz, of the generating function for the generalized twisted Bernoulli polynomials and the quotient of p-adic integrals that can be expressed as the exponential generating function for the generalized twisted power sums.

TRIPLE SYMMETRIC IDENTITIES FOR w-CATALAN POLYNOMIALS

  • Kim, Dae San;Kim, Taekyun
    • Journal of the Korean Mathematical Society
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    • v.54 no.4
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    • pp.1243-1264
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    • 2017
  • In this paper, we introduce w-Catalan polynomials as a generalization of Catalan polynomials and derive fourteen basic identities of symmetry in three variables related to w-Catalan polynomials and analogues of alternating power sums. In addition, specializations of one of the variables as one give us new and interesting identities of symmetry even for two variables. The derivations of identities are based on the p-adic integral expression for the generating function of the w-Catalan polynomials and the quotient of p-adic integrals for that of the analogues of the alternating power sums.

THE q-ANALOGUE OF TWISTED LERCH TYPE EULER ZETA FUNCTIONS

  • Jang, Lee-Chae
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.6
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    • pp.1181-1188
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    • 2010
  • q-Volkenborn integrals ([8]) and fermionic invariant q-integrals ([12]) are introduced by T. Kim. By using these integrals, Euler q-zeta functions are introduced by T. Kim ([18]). Then, by using the Euler q-zeta functions, S.-H. Rim, S. J. Lee, E. J. Moon, and J. H. Jin ([25]) studied q-Genocchi zeta functions. And also Y. H. Kim, W. Kim, and C. S. Ryoo ([7]) investigated twisted q-zeta functions and their applications. In this paper, we consider the q-analogue of twisted Lerch type Euler zeta functions defined by $${\varsigma}E,q,\varepsilon(s)=[2]q \sum\limits_{n=0}^\infty\frac{(-1)^n\epsilon^nq^{sn}}{[n]_q}$$ where 0 < q < 1, $\mathfrak{R}$(s) > 1, $\varepsilon{\in}T_p$, which are compared with Euler q-zeta functions in the reference ([18]). Furthermore, we give the q-extensions of the above twisted Lerch type Euler zeta functions at negative integers which interpolate twisted q-Euler polynomials.