Analytic functions over Z p and p-regular sequences
Zhang Shu, Jia-Yan Yao · Comptes Rendus Mathématique · 2011
Let p be a prime number. In this work we characterize all the analytic functions f : Z p → C p without roots in N for which the sequence ( v p ( f ( n ) ) ) n ≥ 0 is p -regular. Then we apply our characterization to study quadratic linear recurrent sequences.