
Asymptotically automatic sequences generalize the notion of automatic sequences by relaxing the requirement of finite k-kernels to finite up to asymptotic equality. This paper systematically investigates the properties of asymptotically automatic sequences and establishes analogues or counterparts to various well-known facts about automatic sequences.


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asymptotically-automatic-sequences-generalizing-automatic-sequences-and-their-properties


Asymptotically Automatic Sequences: Generalizing Automatic Sequences and Their Properties


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Weil sums of binomials with four distinct values must be rational integers, except in the case where the finite field has order 5 and the exponent is congruent to 3 modulo 4.


rationality-of-weil-sums-of-binomials-with-four-distinct-values


Rationality of Weil Sums of Binomials with Four Distinct Values
