Duke Mathematical Journal

Relating invariant linear form and local epsilon factors via global methods

Dipendra Prasad and Hiroshi Saito

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We use the recent proof of Jacquet's conjecture due to Harris and Kudla [HK] and the Burger-Sarnak principle (see [BS]) to give a proof of the relationship between the existence of trilinear forms on representations of ${\rm GL}_2(k_u)$ 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 in [P1, Theorem 1.4]. The method used is very flexible and gives a global proof of a theorem of Saito and Tunnell about characters of ${\rm GL}_2$ using a theorem of Waldspurger [W, Theorem 2] about period integrals for ${\rm GL}_2$ and also an extension of the theorem of Saito and Tunnell by this author in [P3, Theorem 1.2] which was earlier proved only in odd residue characteristic. In the appendix to this article, H. Saito gives a local proof of Lemma 4 which plays an important role in the article

Article information

Duke Math. J. Volume 138, Number 2 (2007), 233-261.

First available in Project Euclid: 5 June 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 22E50: Representations of Lie and linear algebraic groups over local fields [See also 20G05]
Secondary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields


Prasad, Dipendra; Saito, Hiroshi. Relating invariant linear form and local epsilon factors via global methods. Duke Math. J. 138 (2007), no. 2, 233--261. doi:10.1215/S0012-7094-07-13823-7. http://projecteuclid.org/euclid.dmj/1181051031.

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