Abstract:
In this thesis we give an exposition of various known techniques of constructing p-
adic L-functions in different cases. The key idea behind this is constructing a non-
archimedean measure and then performing a p-adic Mellin transform of a suitable
p-adic character. There is also the alternative approach introduced by Iwasawa of
finding a p-adic holomorphic power series interpolating the special values of a Dirichlet L-function. We explain the prerequisites and expand upon above ideas to give a
comprehensive view.
