Nonlocal dynamics of $p$-adic strings

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 the argument of the Riemann zeta function. We present a brief review and some new results.