Summary
Analogs are proved for sequences in Φ=GF[q, x] and Φ′=GF {q, x } of results proved in 1962 by C.L. Vanden Eynden concerning uuiform distribution of sequence of integers related to sequences of real numbers. The concept of uniform distribution (mod m), m an integer, in Vanden Eynden's work is sometimes replaced here by modified forms of uniform distribution (mod M) M ∈ Φ.
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References
L. Carlitz,Diophantine approximation in fields of characteristic p, Trans. Amer. Math. Soc.72 (1951), 187–208.
John H. Hodges,Uniform distribution of sequences in GF[q, x], Acta. Arith.12 (1966), 55–75.
Ivan Nivan,Uniform distribution of sequences of integers, Compositio Math. 16 Fasc. 1,2 (1964), 158–160.
C. L. Vanden Eynden,The uniform distribution of sequences, dissertation, University of Oregon, 1962.
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Supported by NSF Research Grant GP 6515.
Entrata in Redazione il 13 giugno 1969.
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Hodges, J.H. On uniform distribution of sequences inGF {q, x } and [GFq, x]. Annali di Matematica 85, 287–294 (1970). https://doi.org/10.1007/BF02413539
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DOI: https://doi.org/10.1007/BF02413539