We define a topological space over the p-adic numbers, in which Euler products and Dirichlet series converge. We then show how the classical Riemann zeta function has a (p-adic) Euler product structure at the negative integers. Finally, as a corollary of these results, we derive a new formula for the non-Archimedean Euler?Mascheroni constant.
|Pages (from-to)||583 - 606|
|Number of pages||24|
|Journal||Proceedings of the Edinburgh Mathematical Society|
|Publication status||Published - 2009|