On the Periods of Automorphic Forms on Special Orthogonal Groups and the Gross–Prasad Conjecture

By Atsushi Ichino, Tamotsu Ikeda. 2010

173 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d1abab062170311777b76854ca45deb972d35836

How researchers see this paper

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

In Discrete Mathematics and Combinatorics

1. Wei Zhang
2. W. Gan
3. Atsushi Ichino
4. Richard Harris
5. Y. Sakellaridis
6. Abhishek Saha
7. Paul D. Nelson
8. Erez Lapid

In Geometry and Topology

1. Wei Zhang
2. Akshay Venkatesh
3. P. Michel
4. W. Gan
5. Paul D. Nelson
6. Hiraku Atobe
7. Dipendra Prasad
8. Emmanuel Kowalski

In Mathematical Physics

1. Wei Zhang
2. W. Gan
3. Akshay Venkatesh
4. P. Michel
5. Paul D. Nelson
6. Atsushi Ichino
7. Dipendra Prasad
8. Hiraku Atobe

Citations in the corpus

• On endoscopy and the refined Gross–Prasad conjecture for (SO5, SO4) (2010, background): “Their conjecture was refined in [21], where a conjectural formula relating the periods to the central critical L-values was given.”
• 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”
• Equidistribution Of Cusp Forms In The Level Aspect (2010, methodology): “We extend Watson’s result in Theorem 4.1 by computing (Lemma 4.4) a p-adic integral arising in Ichino’s general formula [16], specifically (5) ∫ g∈PGL2(Qp) 〈g · φp, φp〉 〈φp, φp〉 〈g · fp, fp〉 〈fp, fp〉 〈g · fp, fp〉 〈fp, fp〉 dg, where φp (resp. fp) is the newvector at p for the adelization of φ (resp. ”
• Automorphic period and the central value of Rankin--Selberg L-function (2012, background): “[23], [21]) that refines the global Gan–Gross–Prasad conjecture for unitary groups.”
• A Refined Gross-Prasad Conjecture for Unitary Groups (2012, background): “for unramified data φv, fv satisfying conditions (U1)− (U6) in [18].”
• Spherical varieties and integral representations of L-functions (2009, background): “12For the sake of completeness, we should mention that when P comes from a period integral one should in general modify the conjecture above by some “mild” arithmetic factors, such as the sizes of centralizers of Langlands parameters — see [Ichino and Ikeda 2010].”
• The orbit method and analysis of automorphic forms (2018, background): “The definition of L(Π,Σ) then applies, at least for tempered Π and Σ, and one expects L(Π,Σ) to be related to special values of L-functions: Ichino–Ikeda [43] and N.”
• A conjecture on Whittaker-Fourier coefficients of cusp forms (2013, result): “d to make the following: Conjecture 1.1. For any elliptic Arthur’s parameter φof Ramanujan type we have cψN πψN(φ) = |Sφ|. The conjecture is inspired by recent conjectures and results of Ichino–Ikeda [II10] which sharpen the Gross–Prasad conjecture. (See [GGP12] for a recent extension of these conje”
• Local theta correspondence of tempered representations and Langlands parameters (2016, result): “re exists π′ ∈Irrtemp(G′(Wn)) such that HomG(W n)(π⊗π ′,ω) 6= 0 . Proof. The proof is similar to that of Lemma 12.5 in [GS]. The absolutely convergence of double integrals which we need are proven in [II] for orthogonal cases, [Ha] for hermitian cases, [X2] for symplectic-metaplectic cases, and [X1]”
• Local spectral equidistribution for Siegel modular forms and applications (2010, result): “It is also compatible with a conjecture of Prasad and Takloo–Bighash [39], which itself is an analogue (for the case of Bessel periods) of the remarkable Ichino-Ikeda conjecture [21] dealing with (SO(n), SO(n − 1)) periods.”
• Fourier transform and the global Gan–Gross–Prasad conjecture for unitary groups (2014, methodology): “In the 1990’s, Gross and Prasad formulated a conjectural generalization of Waldspurger’s work to higher rank orthogonal groups ([21], [22]) (later refined by Ichino–Ikeda [31]).”
• Spherical functions on spherical varieties (2009, methodology): “composed an unramified representation πof Gas π1⊗π2 according to the decomposition G = SOn ×SOn+1. In this case our calculation is similar to that performed (in greater generality) by Ichino and Ikeda [II]. 7.2.6. Example. Let X = GLn \SO2n+1, where nis an even number. Here we have Gˇ X = Spn ×Spn ⊂ ”