  We consider the construction of Lagrangians that might be suitable for
describing the entire $p$-adic sector of an adelic open scalar string. These
Lagrangians are constructed using the Lagrangian for $p$-adic strings with an
arbitrary prime number $p$. They contain space-time nonlocality because of the
d'Alembertian in argument of the Riemann zeta function. We present a brief
review and some new results.
