Relating invariant linear form and local epsilon factors via global methods

2005/12/07 by Dipendra Prasad, Prasad, Dipendra · 3 citations
Computer Science · Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Mathematical Analysis and Transform Methods #Matrix Theory and Algorithms #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0512151

openalex publication_date 2005/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use the recent proof of Jacquet's conjecture due to Harris and Kudla, and the Burger-Sarnak principle to give a proof about the relationship between the existence of trilinear forms on representations of GL₂(k_u) for a non-Archimedean local field k_u and local epsilon factors which was earlier proved only in the odd residue characteristic by this author. The same method gives a global proof of a theorem of Saito and Tunnell about characters of GL₂ using a theorem of Waldspurger about period integrals for GL₂ and also an extension of the theorem of Saito-Tunnell by this author which was earlier proved only in odd residue characteristic.

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