2019/09/19 by Alexandru Chirvăsitu, Chirvasitu, Alexandru, Thomas W. Cusick +1
Computer Science · Mathematics · #06E30 #11G20 #37B50 #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1910.01908
openalex publication_date 2019/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We identify the weights wt(fn) of a family \fn\ of rotation symmetric Boolean functions with the cardinalities of the sets of n-periodic points of a finite-type shift, recovering the second author's result that said weights satisfy a linear recurrence. Similarly, the weights of idempotent functions fn defined on finite fields can be recovered as the cardinalities of curves over those fields and hence satisfy a linear recurrence as a consequence of the rationality of curves' zeta functions. Weil's Riemann hypothesis for curves then provides additional information about wt(fn). We apply our results to the case of quadratic functions and considerably extend the results in an earlier paper of ours.