2017
DOI: 10.2140/ant.2017.11.253
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Test vectors and central L-values for GL(2)

Abstract: We determine local test vectors for Waldspurger functionals for GL 2 , in the case where both the representation of GL 2 and the character of the degree two extension are ramified, with certain restrictions. We use this to obtain an explicit version of Waldspurger's formula relating twisted central L-values of automorphic representations on GL 2 with certain toric period integrals. As a consequence, we generalize an average value formula of Feigon and Whitehouse, and obtain some nonvanishing results. 1

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Cited by 23 publications
(50 citation statements)
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“…where we have L(1/2, π E ⊗ Ω) = 0 for those π ∈ F new (2k, N) − F new (2k, N, Θ). We remark that for Σ 3 = ∅, a much wider result has been obtained by File, Martin and Pitale in [3], where they determined the local test vectors for Waldspurger functionals for GL 2 . Assume Σ 3 = ∅.…”
Section: Introductionmentioning
confidence: 57%
“…where we have L(1/2, π E ⊗ Ω) = 0 for those π ∈ F new (2k, N) − F new (2k, N, Θ). We remark that for Σ 3 = ∅, a much wider result has been obtained by File, Martin and Pitale in [3], where they determined the local test vectors for Waldspurger functionals for GL 2 . Assume Σ 3 = ∅.…”
Section: Introductionmentioning
confidence: 57%
“…Acknowledgments We thank Jeanine van Order for providing us with the reference [11]. While writing this note Santiago Molina informed us that he proved a similar result on the equality of automorphic and algebraic periods.…”
Section: Introductionmentioning
confidence: 75%
“…The second assertion follows from the vanishing criterion of toric periods integrals by Saito and Tunnell (see [18] and [20]). The first assertion is a direct consequence of the calculations in [11].…”
Section: Stickelberger Elements Associated To Automorphic Representatmentioning
confidence: 82%
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