The main conjecture of Iwasawa theory was formulated as an assertion that two ways of defining p-adic L-functions ( by module theory , by interpolation ) should coincide , as far as that was well-defined . The main conjecture of Iwasawa theory was formulated as an assertion that two methods of defining p-adic L-functions ( by module theory , by interpolation ) should coincide , as far as that was well-defined .