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<p>We introduce a new generalization of Euler’s <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\varphi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>φ</mi> </math></EquationSource> </InlineEquation>-function associated with a system of polynomials of several variables. We reprove by a short direct approach certain known related identities, and study some other special cases that do not appear in the literature. We also discuss the unitary analogues of these functions.</p>

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Generalizations of Euler’s \(\varphi \)-function with respect to systems of polynomials of several variables

  • 期刊论文

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  • 发表日期：

    2026年7月17日

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  • Norbert Csizmazia,
  • László Tóth

摘要

We introduce a new generalization of Euler’s \(\varphi \) φ -function associated with a system of polynomials of several variables. We reprove by a short direct approach certain known related identities, and study some other special cases that do not appear in the literature. We also discuss the unitary analogues of these functions.