國立清華大學 數學系

abstract: A Tauberian theorem connects the asymtotic behavior of a positive real sequence with analytic properties of the Dirichlet series associated to this sequence. We are interesting in a function field analogue of the so-called Wiener-Ikehara-Tauberian theorem. Just as the classical Tauberian theorem has various applications in number theory, our version of this theorem adapted to function fields also has numerous applications to arithmetic of function fields. Because Riemman hypothesis is already valid for these function fields, the proof of our Tauberian theorem is simpler. There are particular cases, when we apply our theorem, we get stronger results as compared to what can be done in classical number theory. Tea Time: 3:30PM, R707