TY - JOUR

T1 - The convergence of Euler products over p-adic number fields

AU - Delbourgo, Daniel

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

UR - http://journals.cambridge.org/action/displayIssue?jid=PEM&seriesId=2&volumeId=52&issueId=03&iid=6206072#

M3 - Article

VL - 52

SP - 583

EP - 606

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

SN - 0013-0915

ER -