Abstract:
The frequencies of occurrences of elements in linear recurrence sequences of vectors over Galois rings are studied. The study of these frequencies is reduced to the study of the corresponding trigonometric sums over Galois rings. Based on estimates for trigonometric sums, nontrivial estimates for the frequencies of occurrence of elements in linear recurrence sequences are obtained, which generalize some known results for
sequences over a finite field. These estimates are asymptotically best possible.
Bibliography: 25 titles.
Keywords:linear recurrence sequences, Galois rings, trigonometric sums, distribution of elements of pseudorandom sequences, estimates for trigonometric sums.
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