Abstract
It is shown that if f is any entire function in the class [2,π/2), which along with finitely many of its successive derivatives, vanishes at the integer lattice points, suitably scaled, then f is identically zero. It is then shown that if f is any entire function in a proper subclass of [2,π/2), which along with finitely many of its successive derivatives, is bounded at the integer lattice points, suitably scaled, then f is constant. A heuristic argument in support of the conjecture that this latter result holds for the full class [2, π/2) is given.
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