共轭欧拉函数渐近公式中余项的volterra积分方程

IF 0.2 Q4 MATHEMATICS

JP Journal of Algebra Number Theory and Applications Pub Date : 2022-05-12 DOI:10.17654/0972555522017

Hidetomo Iwata

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引用次数: 1

摘要

。J.Kaczorowski和K.Wiertelak考虑了欧拉φ函数和扭曲欧拉φ函数渐近公式中余项的积分方程。2013年，J.Kaczorowski定义了将上述两个函数扩展的关联欧拉泛函，并证明了其渐近公式。在本文中，我们首先考虑了伴随欧拉函数渐近公式中剩余项的Volterra积分方程。其次，对Volterra积分方程进行求解，并将相关Euler totient函数渐近公式中的误差项分别拆分为算术部分和解析部分。

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ON THE VOLTERRA INTEGRAL EQUATION FOR THE REMAINDER TERM IN THE ASYMPTOTIC FORMULA ON THE ASSOCIATED EULER TOTIENT FUNCTION

. J.Kaczorowski and K.Wiertelak considered the integral equation for remainder terms in the asymptotic formula for the Euler totient function and for the twisted Euler ϕ -function. In 2013, J.Kaczorowski deﬁned the associated Euler totient function which extends the above two functions and proved an asymptotic formula for it. In the present paper, ﬁrst, we consider the Volterra integral equation for the remainder term in the asymptotic formula for the associated Euler totient function. Secondly, we solve the Volterra integral equation and we split the error term in the asymptotic formula for the associated Euler totient function into two sum-mands called arithmetic and analytic part respectively.

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JP Journal of Algebra Number Theory and Applications MATHEMATICS-

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期刊介绍： The JP Journal of Algebra, Number Theory and Applications is a peer-reviewed international journal. Original research papers theoretical, computational or applied, in nature, in any branch of Algebra and Number Theory are considered by the JPANTA. Together with the core topics in these fields along with their interplay, the journal promotes contributions in Diophantine equations, Representation theory, and Cryptography. Realising the need of wide range of information for any emerging area of potential research, the journal encourages the submission of related survey articles as well.