Algorithms to Construct Normal Bases of Cyclic Number Fields Original Research Article

Let K be a cyclic Galois extension of image of finite degree. We give two algorithms to construct a normal basis of K over image. Our proof uses the method developed by S. A. Stepanov and I.E. Shparlinskiy (1989, Mat. Sb.180, 1067-1072) in the case of finite fields. Another tool is a recent estimate of H. P. Schlickewei (Acta Math., to appear) for multiplicities of linear recurrence sequences.