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A divided-difference characterization of polynomials over finite fields of characteristic two
(2022-04-01)
Kim, Veasna
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Laohakosol, Vichian
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Mavecha, Sukrawan
For a finite field F of characteristic 2, an integer n≥ 3 , and for a function f: F→ F, if there is a function h: F→ F such that the divided difference f[x<inf>1</inf>, ⋯ , x<inf>n</inf>] on any n distinct elements of F satisfies f[x<inf>1</inf>, … , x<inf>n</inf>] = h(x<inf>1</inf>+ ⋯ + x<inf>n</inf>) , then f is a polynomial of degree at most n over F. This makes earlier work of Davies and Rousseau complete.
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A class of continuous solutions of a fourth order polynomiallike iterative equation
(2021-07-01)
Thangroongvongthana, Supharerg
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Laohakosol, Vichian
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Mavecha, Sukrawan
Using the so-called characteristic method, continuous solutions of the fourth order polynomial-like iterative equation 4323210 f4(x) + a3f3(x) + a2f2(x) + a1f(x) + a0x=0 were determined subject to certain natural conditions on its characteristic roots. The result so obtained complements earlier work in the cases of second and third order equations.
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Integer factorization and finite Fourier series expansion
(2021-04-01)
Yangklan, Pussadee
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Laohakosol, Vichian
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Mavecha, Sukrawan
Given two integers a and k > 0, the number of factorizations of a (mod k) is the number of ordered pairs (s, t) ∈ {0, 1,.. , k − 1}<sup>2</sup> satisfying s · t ≡ a (mod k). This number is known to be expressible by a formula involving the greatest common divisor function. Motivated by such a formula, we derive several formulae counting the number of factorizations of a (mod k) subject to certain other natural restrictions. Some of these formulae are obtained as consequences of finite Fourier series expansions of the greatest common divisor function, whereas some are shown to be closely connected with the notion of unitary divisors.
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Linear dependence of four types of arithmetic functions
(2019-11-01)
Ponpetch, Kanet
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Laohakosol, Vichian
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Mavecha, Sukrawan
General criteria were derived for the linear dependence of arithmetic functions over the complex field as well as several other criteria for arithmetic functions that were solutions of additive, multiplicative, exponential, and logarithmic equations. A number of examples were worked out in order to compare the results with the existing ones.
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Independence of additive, multiplicative, exponential and logarithmic functions
(2019-10-01)
Ponpetch, Kanet
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Laohakosol, Vichian
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Mavecha, Sukrawan
The independence of four types of functions, namely, additive, multiplicative, exponential and logarithmic functions defined over two types of domains, namely, discrete and non-discrete sets are investigated.
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A system of functional equations satisfied by components of a quadratic function and its stability
(2019-10-01)
Ponpetch, Kanet
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Laohakosol, Vichian
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Mavecha, Sukrawan
A system of functional equations satisfied by the components of a quadratic function is derived via their corresponding circulant matrix. Given such a system of functional equations, general solutions are determined and a stability result for such a system is established.
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Functions with constant sums over a hyperplane and applications
(2019-01-01)
Ponpetch, Kanet
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Mavecha, Sukrawan
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Laohakosol, Vichian
Two functional equations exhibiting functions with constant sums over points lying in a hyperplane are solved, and the results are applied to characterize major trigonometric and hyperbolic functions.
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Functional equations characterizing the sine and cosine functions over a convex polygon
(2019-01-01)
Ponpetch, Kanet
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Laohakosol, Vichian
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Mavecha, Sukrawan
Two functional equations exhibiting functions with a constant sum over points lying in a hyperplane are solved. These functional equations are employed to characterize the sine and cosine functions.
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Iterative roots of some functions
(2018-01-01)
Mavecha, Sukrawan
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Laohakosol, Vichian
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Yuttanan, Boonrod
The iterative equation f<sup>q</sup>(x) = g(x), x ∈ X for a given function g and a positive integer q is solved in the following two main cases: (i) X = ℤ, g(x) = ax + b, ( a, b ∈ ℤ a ≠ 0, 1); (ii) X = ℕ ∪ (0), g is increasing with no fixed point.
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Polynomials with generalized Fibonacci number coefficients
(2017-11-22)
Sitthaset, Airada
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Laohakosol, Vichian
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Mavecha, Sukrawan
Garth, Mills and Mitchell in 2007 started the invesitgation on the nature of real zeros, and the Mahler measures of Fibonacci-coefficient polynomials, which are polynomials whose coefficients are Fibonacci numbers. Their results have later been extended in various directions. We complement these earlier works by investigatiing generalized Fibonacci-coefficient polynomials, which are polynomials whose coefficients are generalized Fibonacci numbers. Our main results give precise information about the location of the real roots of generalized Fibonacci-coefficient polynomials, and the computation of their Mahler measures.

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