Zeta Strings

We introduce nonlinear scalar field models for open and open-closed strings with spacetime derivatives encoded in the operator valued Riemann zeta function. The corresponding two Lagrangians are derived in an adelic approach starting from the exact Lagrangians for effective fields of $p$-adic tachyon strings. As a result tachyons are absent in these models. These new strings we propose to call zeta strings. Some basic classical properties of the zeta strings are obtained and presented in this paper.