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Letj  ⁢   (  z  ){j(z)}    be the modular  j -invariant function. Let τ be an algebraic number in the complex upper half planeℍ{\mathbb{H}}   . It was proved by Schneider and Siegel that if τ is not a CM point, i.e.,[  ℚ   (  τ  )   :  ℚ  ]   ≠  2{[\mathbb{Q}(\tau):\mathbb{Q}]\neq 2}   , thenj  ⁢   (  τ  ){j(\tau)}    is transcendental. Let  f  be a harmonic weak Maass form of weight 0 onΓ  0   ⁢   (  N  ){\Gamma_{0}(N)}   . In this paper, we consider an extension of the results of Schneider and Siegel to a family of values of  f  on Hecke orbits of τ. For a positive integer  m , letT  m{T_{m}}    denote the  m -th Hecke operator. Suppose that the coefficients of the principal part of  f  at the cuspi  ⁢  ∞{i\infty}    are algebraic, and that  f  has its poles only at cusps equivalent toi  ⁢  ∞{i\infty}   . We prove, under a mild assumption on  f , that, for any fixed τ, if  N  is a prime such thatN  ≥  23{N\geq 23}    andN  ∉   {  23  ,  29  ,  31  ,  41  ,  47  ,  59  ,  71  }{N\notin\{23,29,31,41,47,59,71\}}   , thenf   (   T  m   .  τ  ){f(T_{m}.\tau)}    are transcendental for infinitely many positive integers  m  prime to  N .

Schneider–Siegel theorem for a family of values of a harmonic weak Maass form at Hecke orbits