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On differential independence of $\boldsymbol{\zeta }$ and ${\boldsymbol{\varGamma }}$

Volume 124 / 2020

Qi Han, Jingbo Liu Annales Polonici Mathematici 124 (2020), 151-159 MSC: Primary 11M06, 33B15; Secondary 26B05, 30D30, 34M15. DOI: 10.4064/ap190621-17-9 Published online: 9 January 2020

Abstract

We prove that $\boldsymbol {\zeta }$ and $\boldsymbol {\Gamma }$ cannot satisfy any differential equation generated by a function from a family of functions continuous in $\boldsymbol {\zeta },\boldsymbol {\zeta }’,\ldots ,\boldsymbol {\zeta }^{(m)}$ and polynomial in $\boldsymbol {\Gamma },\boldsymbol {\Gamma }’,\ldots ,\boldsymbol {\Gamma }^{(n)}$.

Authors

  • Qi HanDepartment of Science and Mathematics
    Texas A&M University
    San Antonio, TX 78224, U.S.A.
    e-mail
  • Jingbo LiuDepartment of Science and Mathematics
    Texas A&M University
    San Antonio, TX 78224, U.S.A.
    e-mail

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