A p-adic Eisenstein measure for unitary groups
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Ellen E. Eischen
Abstract
We construct a p-adic Eisenstein measure with values in the space of p-adic automorphic forms on certain unitary groups. Using this measure, we p-adically interpolate certain special values of both holomorphic and non-holomorphic Eisenstein series, as both the archimedean and the p-adic weights of the Eisenstein series vary.
Funding source: National Science Foundation
Award Identifier / Grant number: DMS-1249384
I am grateful to Matthew Emerton and Christopher Skinner for insightful suggestions during the past year, especially as I came across modifications that I needed to make to [Doc. Math., J. DMV Extra (2006), 393–464]. Many of the suggestions found their way into Section 2.2.8. I am grateful to Michael Harris for helpful discussions, responses to my questions, and encouragement to complete this project, as well as enthusiastic suggestions for subsequent related projects. I would also like to thank the anonymous referee, for helpful comments and for suggesting that I add some remarks on functional equations (in analogue with the development in [Invent. Math. 49 (1978), no. 3, 199–297]). I thank Mark Behrens for answering my questions about the conjectured implications of the p-adic Eisenstein series for homotopy theory. I would also like to thank both Harris and Behrens for alerting me, in the first place, to the role of p-adic Eisenstein series in homotopy theory. This project relies upon the ideas in Nicholas Katz's construction of Eisenstein measures, without which the current project would be impossible. This paper also relies heavily upon the helpfully detailed presentation of C∞-Eisenstein series in Goro Shimura's papers; if Shimura's writing had not been so precise, I would have struggled much more with the non-p-adic portion of this project.
© 2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- Relatively very free curves and rational simple connectedness
- Moduli of unipotent representations II: Wide representations and the width
- Analog of selfduality in dimension nine
- A p-adic Eisenstein measure for unitary groups
- On the Kähler–Ricci flow near a Kähler–Einstein metric
- Homogeneous Ricci solitons
- Energy inequalities for cutoff functions and some applications
- Dimension of elementary amenable groups
Articles in the same Issue
- Frontmatter
- Relatively very free curves and rational simple connectedness
- Moduli of unipotent representations II: Wide representations and the width
- Analog of selfduality in dimension nine
- A p-adic Eisenstein measure for unitary groups
- On the Kähler–Ricci flow near a Kähler–Einstein metric
- Homogeneous Ricci solitons
- Energy inequalities for cutoff functions and some applications
- Dimension of elementary amenable groups
