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Construction of $p$-adic $L$-functions for unitary groups

By Michael Harris

Appears in collection : Arithmetic geometry, representation theory and applications / Géométrie arithmétique, théorie des représentations et applications

This is a report on the construction of $p$-adic $L$-functions attached to ordinary families of holomorphic modular forms on the unitary groups of $n$-dimensional hermitian vector spaces over $CM$ fields. The results have been obtained over a period of nearly 15 years in joint work with Ellen Eischen, Jian-Shu Li, and Chris Skinner. The $p$-adic $L$-functions specialize at classical points to critical values of standard $L$-functions of cohomological automorphic forms on unitary groups, or equivalently of cohomological automorphic forms on $GL(n)$ that satisfy a polarization condition. When $n = 1$ one recovers Katz's construction of $p$-adic $L$-functions of Hecke characters.

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Citation data

  • DOI 10.24350/CIRM.V.18774303
  • Cite this video Harris Michael (6/22/15). Construction of $p$-adic $L$-functions for unitary groups. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18774303
  • URL https://dx.doi.org/10.24350/CIRM.V.18774303

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Bibliography

  • Harris, M., Li, J.-S., & Skinner, C.M. (2006). $p$-adic $L$-functions for unitary Shimura varieties. I: Construction of the Eisenstein measure. Documenta Mathematica, Extra Vol., 393-464 - http://eudml.org/doc/129180

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