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A note on the Demjanenko matrices related to the cyclotomic $\mathbf {Z}_p$-extension

A note on the Demjanenko matrices related to the cyclotomic $\mathbf {Z}_p$-extension

In this note, we define the Demjanenko matrices related to the cyclotomic Z pextension, which can be regarded as generalization of the ordinary Demjanenko matrices.As a special case, we generalize the Maillet determinant defined by Girstmair.