Asymptotic behavior of supercuspidal representations and Sato-Tate equidistribution for families
© 2019 The Authors We establish properties of families of automorphic representations as we vary prescribed supercuspidal representations at a given finite set of primes. For the tame supercuspidals constructed by J.-K. Yu we prove the limit multiplicity property with error terms. Thereby we obtain...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier BV
2021
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| Online Access: | https://hdl.handle.net/1721.1/136587 |
| _version_ | 1811097602210398208 |
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| author | Kim, Ju-Lee Shin, Sug Woo Templier, Nicolas |
| author_facet | Kim, Ju-Lee Shin, Sug Woo Templier, Nicolas |
| author_sort | Kim, Ju-Lee |
| collection | MIT |
| description | © 2019 The Authors We establish properties of families of automorphic representations as we vary prescribed supercuspidal representations at a given finite set of primes. For the tame supercuspidals constructed by J.-K. Yu we prove the limit multiplicity property with error terms. Thereby we obtain a Sato-Tate equidistribution for the Hecke eigenvalues of these families. The main new ingredient is to show that the orbital integrals of matrix coefficients of tame supercuspidal representations with increasing formal degree on a connected reductive p-adic group tend to zero uniformly for every noncentral semisimple element. |
| first_indexed | 2024-09-23T17:02:10Z |
| format | Article |
| id | mit-1721.1/136587 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T17:02:10Z |
| publishDate | 2021 |
| publisher | Elsevier BV |
| record_format | dspace |
| spelling | mit-1721.1/1365872021-10-28T03:03:14Z Asymptotic behavior of supercuspidal representations and Sato-Tate equidistribution for families Kim, Ju-Lee Shin, Sug Woo Templier, Nicolas © 2019 The Authors We establish properties of families of automorphic representations as we vary prescribed supercuspidal representations at a given finite set of primes. For the tame supercuspidals constructed by J.-K. Yu we prove the limit multiplicity property with error terms. Thereby we obtain a Sato-Tate equidistribution for the Hecke eigenvalues of these families. The main new ingredient is to show that the orbital integrals of matrix coefficients of tame supercuspidal representations with increasing formal degree on a connected reductive p-adic group tend to zero uniformly for every noncentral semisimple element. 2021-10-27T20:36:08Z 2021-10-27T20:36:08Z 2020 2021-05-24T14:43:10Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/136587 en 10.1016/J.AIM.2019.106955 Advances in Mathematics Creative Commons Attribution 4.0 International license https://creativecommons.org/licenses/by/4.0/ application/pdf Elsevier BV Elsevier |
| spellingShingle | Kim, Ju-Lee Shin, Sug Woo Templier, Nicolas Asymptotic behavior of supercuspidal representations and Sato-Tate equidistribution for families |
| title | Asymptotic behavior of supercuspidal representations and Sato-Tate equidistribution for families |
| title_full | Asymptotic behavior of supercuspidal representations and Sato-Tate equidistribution for families |
| title_fullStr | Asymptotic behavior of supercuspidal representations and Sato-Tate equidistribution for families |
| title_full_unstemmed | Asymptotic behavior of supercuspidal representations and Sato-Tate equidistribution for families |
| title_short | Asymptotic behavior of supercuspidal representations and Sato-Tate equidistribution for families |
| title_sort | asymptotic behavior of supercuspidal representations and sato tate equidistribution for families |
| url | https://hdl.handle.net/1721.1/136587 |
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