• Journal of the Chungcheong Mathematical Society
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• v.28 no.1
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• pp.83-88
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• 2015

In this paper we give a determinant formula for the relative congruent zeta function in cyclotomic function fields.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.455-464
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• 2012

In the previous paper [8], the author gave a determinant formula of relative zeta function for cyclotomic function fields. Our purpose of this paper is to extend this result for more general function fields. As an application of our formula, we will give determinant formulas of class numbers for constant field extensions.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.203-210
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• 1997

We give some interesting identities involving the Hurwitz and Riemann zeta functions.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1425-1432
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• 2014

The Euler zeta function is defined by ${\zeta}_E(s)=\sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{n^8}$. The purpose of this paper is to find formulas of the Euler zeta function's values. In this paper, for $s{\in}\mathbb{N}$ we find the recurrence formula of ${\zeta}_E(2s)$ using the Fourier series. Also we find the recurrence formula of $\sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{(2_{n-1})^{2s-1}}$, where $s{\geq}2({\in}\mathbb{N})$.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1219-1224
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• 2011

In this paper we give a determinant formula for congruent zeta functions of real Abelian function fields. We also give some example of congruent zeta functions when the conductor of real Abelian function field is monic irreducible.

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.435-443
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• 1998

Some mathematical constants have been used in evaluating series involving the Zeta function, the origin of which can be traced back to an over two centries old theorem of Christian Goldbach. We show some of the series involving the Zeta function can be evaluated in terms of the Catalan's constant by using the theory of the double Gamma function.

• East Asian mathematical journal
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• v.34 no.3
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• pp.287-293
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• 2018

We investigate the averaging value of a random sampling ${\zeta}(1/2+iX_t)$ of the Riemann zeta function on the critical line. Our result is that if $X_t$ is an increasing random sampling with Poisson distribution, then $${\mathbb{E}}{\zeta}(1/2+iX_t)=O({\sqrt{\;log\;t}}$$, for all sufficiently large t in ${\mathbb{R}}$.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.287-304
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• 2017

Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [Integral Transforms Spec. Funct. 23 (2012), 659-683] by means of the incomplete Pochhammer symbols $({\lambda};{\kappa})_{\nu}$ and $[{\lambda};{\kappa}]_{\nu}$, we first introduce incomplete Fox-Wright function. We then define the families of incomplete extended Hurwitz-Lerch Zeta function. We then systematically investigate several interesting properties of these incomplete extended Hurwitz-Lerch Zeta function which include various integral representations, summation formula, fractional derivative formula. We also consider an application to probability distributions and some special cases of our main results.

• Kyungpook Mathematical Journal
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• v.63 no.3
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• pp.485-506
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• 2023

This paper investigates an extended form Hurwitz-Lerch zeta function, as well as related integral images, ordinary and fractional derivatives, and series expansions, using the term extended beta function. We establish a connection between the extended Hurwitz-Lerch zeta function and the Laguerre polynomials. Furthermore, we present a probability distribution application of the extended Hurwitz-Lerch zeta function ζ^𝛿,𝜇_𝜈,λ. Several results, both known and new, are shown to follow as special cases of our findings.

• Korean Journal of Mathematics
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• v.28 no.1
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• pp.123-136
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• 2020

In this paper, we give an explicit formula as a rational function for the Ihara zeta function of every finite connected graph without degree one vertices whose circuit rank is two.