  This Ph.D. thesis, prepared under the supervision of Professor Ivan Fesenko,
defines new zeta functions in a nonstandard setting and their analytical
properties are developed. Further, p-adic interpolation is presented within a
nonstandard setting which enables the concept of interpolating with respect to
two, or more, distinct primes to be defined.
  The final part of the dissertation examines the work of M. J. Shai Haran and
makes initial attempts of viewing it from a nonstandard perspective.
