Algebraic independence of the values of the Hecke–Mahler series and its derivatives at algebraic numbers

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  • Taka-aki Tanaka
    Department of Mathematics, Keio University, Hiyoshi 3-14-1, Kohoku-ku, Yokohama 223-8522, Japan
  • Yusuke Tanuma
    Department of Mathematics, Keio University, Hiyoshi 3-14-1, Kohoku-ku, Yokohama 223-8522, Japan

Abstract

<jats:p> We show that the Hecke–Mahler series, the generating function of the sequence [Formula: see text] for [Formula: see text] real, has the following property: Its values and its derivatives of any order, at any nonzero distinct algebraic numbers inside the unit circle, are algebraically independent if [Formula: see text] is a quadratic irrational number satisfying a suitable condition. </jats:p>

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