Abstract
In the first part of this short note we give an answer to a question asked by Franz J. Schnitzer (Leoben). Let \( {({\alpha _k})_{k \geqslant 1}} \) denote the sequence of positive zeroes of the Bessel function J 0(x) in increasing order. We consider the triangular arrays \( ({x_{kN}}) = \left( {\frac{{{\alpha _k}}}{{{\alpha _N}}}} \right),1 \leqslant k \leqslant N,N \in N \) in [0,1). F.J. Schnitzer (personal communication) has conjectured that this triangular array is uniformly distributed modulo 1, i.e.
for any subinterval \( I \subseteq [0,1) \) of length ∣I∣.
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Tichy, R.F. (1998). Three Examples of Triangular Arrays with Optimal Discrepancy and Linear Recurrences. In: Bergum, G.E., Philippou, A.N., Horadam, A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5020-0_46
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