• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.845-871
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• 2020

We consider generalized Dedekind sums in dimension n, defined as sum of products of values of periodic Bernoulli functions. For the generalized Dedekind sums, we associate a Laurent polynomial. Using this, we associate an exponential sum of a Laurent polynomial to the generalized Dedekind sums and show that this exponential sum has a nontrivial bound that is sufficient to fulfill the equidistribution criterion of Weyl and thus the fractional part of the generalized Dedekind sums are equidistributed in ℝ/ℤ.

• Journal of the Korean Mathematical Society
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• v.52 no.3
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• pp.537-565
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• 2015

In this paper, we give relationship between Bernoulli-Euler polynomials and convolution sums of divisor functions. First, we establish two explicit formulas for certain combinatoric convolution sums of divisor functions derived from Bernoulli and Euler polynomials. Second, as applications, we show five identities concerning the third and fourth-order convolution sums of divisor functions expressed by their divisor functions and linear combination of Bernoulli or Euler polynomials.

• East Asian mathematical journal
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• v.36 no.3
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• pp.425-435
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• 2020

We explore the Pauli table C^(-1) and nonzero Pauli table W. Recurrence rules and interrelationships of any k slope diagonal sums over C^(-1) and W are studied in connection with diagonal sums of the Pascal table C⁽¹⁾. Since diagonal sums of C⁽¹⁾ are Fibonacci numbers, any k slope diagonal sums over C^(-1) and W are explained by Fibonacci numbers.

• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.483-492
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• 2009

In this paper we give formulae for sums of products of two Horadam type generalized Fibonacci numbers with the same recurrence equation and with possibly different initial conditions. Analogous improved alternating sums are also studied as well as various derived sums when terms are multiplied either by binomial coefficients or by members of the sequence of natural numbers. These formulae are related to the recent work of Belbachir and Bencherif, $\v{C}$erin and $\v{C}$erin and Gianella.

• Korean Journal of Mathematics
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• v.26 no.3
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• pp.519-535
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• 2018

Let ${\mathcal{R}}$ denote the Galois ring of characteristic $p^n$, where p is a prime. In this paper, we investigate the elementary properties of Gauss sums over ${\mathcal{R}}$ in accordance with conditions of characters of Galois rings, and we restate results for Gauss sums in [1, 2, 3, 7, 12, 13]. Also, we compute the modulus of the Gauss sums.

• Journal of the Korean Mathematical Society
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• v.47 no.5
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• pp.947-965
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• 2010

The main purpose of this paper is using estimates for character sums and analytic methods to study the mean value involving the incomplete character sums, 2-th power mean of the inversion of Dirichlet L-function and general Kloosterman sums, and give four interesting asymptotic formulae for it.

• Kyungpook Mathematical Journal
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• v.50 no.3
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• pp.433-445
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• 2010

Although, interesting properties on the partial sums of analytic univalent functions have been investigated extensively by several researchers, yet analogous results on partial sums of harmonic univalent functions have not been so far explored. The main purpose of the present paper is to establish some new and interesting results on the ratio of starlike harmonic univalent function to its sequences of partial sums.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.1-10
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• 2009

Main purpose of this paper is to define an elliptic analogue of the Hardy sums. Some results, which are related to elliptic analogue of the Hardy sums, are given.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.451-458
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• 2013

The main purpose of this paper is using the analytic methods and the properties of Gauss sums to study the computational problem of one kind mean value of the generalized Kloosterman sums and Dirichlet character of polynomials, and give an interesting asymptotic formula for it.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.449-457
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• 2017

In this paper, we shall provide several properties of Dedekind sums with quasi-periodicity Euler functions. In particular, we present a representation of these Dedekind sums in terms of the Eulerian functions and the tangent functions.