Langlands' analytic continuation and functional equation conjecture for automorphic L-functions
Langlands' analytic continuation and functional equation conjecture for automorphic L-functions
Let be a number field, let be its ring of adeles, let be a connected linear algebraic group defined over , let be an automorphic representation of , and let be a finite-dimensional representation of the Langlands dual group . The associated Langlands -function is denoted by . Langlands' conjecture. The -function has a meromorphic continuation to the whole complex plane with only finitely many poles, and it satisfies a functional equation relating to . This is a foundational analytic expectation for automorphic -functions and generalizes the continuation and functional equation known for classical zeta and Dirichlet -functions. The candidate is not accompanied by evidence of resolution in the supplied text.
Sources & referencesView supporting material
Primary source
Fangyang Tian, “On the Archimedean Local Gamma Factors for Adjoint Representation of GL_3, Part I”, arXiv:1811.02752 (2018).
Additional references
2 papers in this index state this conjecture (2015–2018). The statement above is taken from the most recent of them; the others are arXiv:1506.09128.
Progress summary
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