• Journal of applied mathematics & informatics
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• v.41 no.6
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• pp.1227-1235
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• 2023

The study of convolution sums for divisor functions is an area that has been extensively researched by many mathematicians including Ramanujan. The aim of this paper is to find the formula for convolution sum of divisor functions with coprime conditions.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.277-283
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• 2008

The paper deals with the values at the negative integers of a certain Dirichlet series related to the Riemann zeta function and with the expression of these values in terms of Bernoulli numbers.

• Journal of applied mathematics & informatics
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• v.41 no.3
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• pp.553-567
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• 2023

There are real life situations in our lives where the things are changing continuously or from time to time. It is a very important problem for one whether to continue the existing relationship or to form a new one after some occasions. That is, people, companies, cities, countries, etc. may change their opinion or position rapidly. In this work, we think of the problem of changing relationships from a mathematical point of view and think of an answer. In some sense, we comment these changes as power changes. Our number theoretical model will be based on this idea. Using the convolution sum of the restricted divisor function E, we obtain the answer to this problem.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.419-426
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• 2009

In expansion of function by special basis functions, properties of expansion kernel are very important. In the Fourier series, the series are expressed by the convolution with Dirichlet kernel. We investigate some of properties of kernel in wavelet expansions both in one and higher dimensions.

• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.435-446
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• 2018

Using the theory of combinatoric convolution sums, we establish some arithmetic identities involving Liouville functions and restricted divisor functions. We also prove some relations involving restricted divisor functions and Stirling numbers of the first kind for divisor functions.