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Relative Functoriality and Functional Equations via Trace Formulas

icon-email Yiannis Sakellaridis

Abstract

Langlands’ functoriality principle predicts deep relations between the local and automorphic spectra of different reductive groups. This has been generalized by the relative Langlands program to include spherical varieties, among which reductive groups are special cases. In the philosophy of Langlands’ “beyond endoscopy” program, these relations should be expressed as comparisons between different trace formulas, with the insertion of appropriate L-functions. The insertion of L-functions calls for one more goal to be achieved: the study of their functional equations via trace formulas.

The goal of this article is to demonstrate this program through examples, indicating a local-to-global approach as in the project of endoscopy. Here, scalar transfer factors are replaced by “transfer operators” or “Hankel transforms” which are nice enough (typically, expressible in terms of usual Fourier transforms) that they can be used, in principle, to prove global comparisons (in the form of Poisson summation formulas). Some of these examples have already appeared in the literature; for others, the proofs will appear elsewhere.

Viện Toán học, Viện Hàn lâm Khoa học và Công nghệ Việt Nam

Địa chỉ: Số 18 đường Hoàng Quốc Việt, quận Cầu Giấy, Hà Nội

Điện thoại: 024 37563474 - Fax: 024 37564303

Email: vientoan@math.ac.vn

Viện nghiên cứu cao cấp về toán Hội Toán học Mỹ MathScinet Thư viện số (VAST) Arxiv
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      • 19. /app/Repositories/Pages/PagesRepository.php:108
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      Metadata
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      • 19. /app/Repositories/Pages/PagesRepository.php:108
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      Metadata
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      Metadata
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      Metadata
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      • 19. /app/Repositories/Pages/PagesRepository.php:108
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
      Backtrace
      • 19. /app/Repositories/Pages/PagesRepository.php:108
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      Metadata
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      Metadata
      Backtrace
      • 19. /app/Repositories/Pages/PagesRepository.php:108
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      Metadata
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      Metadata
      Backtrace
      • 19. /app/Repositories/Pages/PagesRepository.php:108
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      Metadata
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      Metadata
      Backtrace
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      Metadata
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      Metadata
      Backtrace
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      Metadata
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      Metadata
      Backtrace
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      Metadata
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      • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
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      Metadata
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