Description:
<jats:p>H. P. F. Swinnerton-Dyer determined the structure of the algebra of modular forms mod <jats:italic>p</jats:italic> for all prime numbers <jats:italic>p</jats:italic> in elliptic modular case (cf. [10]). Using his result, J.-P. Serre investigated the properties of <jats:italic>p</jats:italic>-adic modular forms and succeeded to construct the <jats:italic>p</jats:italic>-adic zeta functions for any totally real number fields (cf. [8]).</jats:p>