Trilinear forms and the central values of triple product $L$-functions

By Atsushi Ichino. 2008

163 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fade6f3e6add9ec489ef7fe940d32685a0ca8477

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Akshay Venkatesh
2. Wei Zhang
3. Paul D. Nelson
4. W. Gan
5. Richard Harris
6. P. Michel
7. Atsushi Ichino
8. Shou-wu Zhang

In Geometry and Topology

1. Akshay Venkatesh
2. Wei Zhang
3. Paul D. Nelson
4. W. Gan
5. P. Michel
6. Atsushi Ichino
7. Richard Harris
8. V. Blomer

In Mathematical Physics

1. Wei Zhang
2. Paul D. Nelson
3. Akshay Venkatesh
4. W. Gan
5. P. Michel
6. Atsushi Ichino
7. Richard Harris
8. V. Blomer

Citations in the corpus

• The subconvexity problem for GL2 (2009, background): “It has been observed J.-L. Waldspurger [69] and greatly extended by Ichino-Ikeda [32,33] that a wide variety of period functionals can be expressed by integrating matrix coefficients; roughly speaking, there exists a variety of pairs (H ⊂ G) so that, with suitable choice of measure and suitable regu”
• On endoscopy and the refined Gross–Prasad conjecture for (SO5, SO4) (2010, methodology): “This refined conjecture follows from a result of Waldspurger [55] for n = 3 and that of the second author [20] for n = 4.”
• On arithmetic fundamental lemmas (2012, background): “Among them we have a by-nomeans complete list: Waldspurger’s work on SO(2) × SO(3) [24], Ichino’s work on SO(3) × SO(4) ([12] etc.”
• Fourier transform and the global Gan–Gross–Prasad conjecture for unitary groups (2014, unknown): “In the lower rank cases, a lot of works have been done on the global Gan–Gross–Prasad conjecture for orthogonal groups: the work of Waldspurger on SOp2q ˆ SOp3q ([56]), the work of Garrett ([16]), Piatetski-Shapiro–Rallis, Garret–Harris, Harris–Kudla ([24]), Gross–Kudla ([20]), and Ichino ([30]) on ”
• Automorphic period and the central value of Rankin--Selberg L-function (2012, methodology): “Ichino and Ikeda first consider the following integration of the matrix coefficient: for φv, ϕv ∈ πv, we define when πv is tempered, αv(φv, ϕv) = ∫ Hv 〈πv(h)φv, ϕv〉v dh, Hv = H(Fv).”
• Equidistribution Of Cusp Forms In The Level Aspect (2010, methodology): “nly when (the factorizable automorphic representations generated by) the three forms are special at p; Harris and Kudla had already considered the case that all three forms are spherical at p. Ichino [16] showed that the local zeta integrals of Harris and Kudla are equal to simpler integrals over th”
• A Refined Gross-Prasad Conjecture for Unitary Groups (2012, background): “In [20], Ichino proves: ∣∣∣∣∫ PB×(F )\PB×(AF ) (f̃1,Σ1 f̃2,Σ2 f̃3,Σ3)(b) db ∣∣∣∣2 = ζF (2)(2)LF (1/2,Σ′) 8 (∏3i=1 |X(τi)|)LF (1,Σ′,Ad) ∏”