Hostname: page-component-7bb8b95d7b-lvwk9 Total loading time: 0 Render date: 2024-10-04T03:58:08.170Z Has data issue: false hasContentIssue false
  • English
  • Français

The convergence of Euler products over p-adic number fields

Part of: Algebraic number theory: global fields Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  23 September 2009

Daniel Delbourgo
Daniel Delbourgo
Affiliation:
School of Mathematical Sciences, Monash University, Clayton, Melbourne 3800, Australia; Email: ([email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Keywords

number theoryzeta functionsIwasawa theoryp-adic L-functionsEuler products

MSC classification

Secondary: 11R23: Iwasawa theory 11M41: Other Dirichlet series and zeta functions 11R60: Cyclotomic function fields (class groups, Bernoulli objects, etc.)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 3 , October 2009 , pp. 583 - 606
Copyright
Copyright © Edinburgh Mathematical Society 2009