Part I Analytic continuation of some zeta functions

摘要

The contents of this paper were presented as lectures at the Miura Winter School on Zeta and L-functions held in 2008. Though the analytic continuation of zeta functions beyond its region of absolute convergence is a fundamental question, in general not much is known about the conditions that guarantee a meromorphic continuation. It is also interesting to know how far such a function can be continued, that is where the natural boundary of analytic continuation lies.