Related papers: A relative trace formula identity for non-tempered…

We propose two families of relative trace formula comparisons in the study of relative Langlands duality conjectured by Ben-Zvi--Sakellaridis--Venkatesh. This allows us to incorporate numerous relative trace formula comparisons studied…

We study a relative trace formula for a compact Riemann surface with respect to a closed geodesic $C$. This can be expressed as a relation between the period spectrum and the ortholength spectrum of $C$. This provides a new proof of…

In this note, we derive explicitly the local relative trace formula for the symmetric space F*\SL(2,F) at the level of Lie algebras, where F is a p-adic field of residue characteristic greater than two and F* is the set of invertible…

We introduce the notion of relative pseudocoefficient for relative discrete series of real spherical homogeneous spaces of reductive groups. We prove that such relative pseudocoefficient does not exist for semisimple symmetric spaces of…

Recent work of Mao, Wan and Zhang \cite{MWZ} has provided a complete list of strongly tempered hyperspherical varieties and they proposed some new period integrals. In this paper, I will present new period integrals of distinguished…

By applying the residue method for period integrals and Langlands-Shahidi's theory for residues of Eisenstein series, we study the period integrals for six spherical varieties. For each spherical variety, we prove a relation between the…

In a companion paper, we formulated a global conjecture for the automorphic period integral associated to the symmetric pairs defined by unitary groups over number fields, generalizing a theorem of Waldspurger's toric period for…

In this paper, we compute the local relative character for 10 strongly tempered spherical varieties in the unramified case. We also study the local multiplicity for these models. By proving a multiplicity formula, we show that the summation…

Let G be a reductive p-adic group. We study how a local Langlands correspondence for irreducible tempered G-representations can be extended to a local Langlands correspondence for all irreducible smooth representations of G. We prove that,…

We study the linear periods on $GL_{2n}$ twisted by a character using a new relative trace formula. We establish the relative fundamental lemma and the transfer of orbital integrals. Together with the spectral isolation technique of…

According to the relative Langlands functoriality conjecture, an admissible morphism between the $L$-groups of spherical varieties should induce a functorial transfer of the corresponding local and global automorphic spectra. Via the…

For the group G=PGL_2 we perform a comparison between two relative trace formulas: on one hand, the relative trace formula of Jacquet for the quotient T\backslash G/T, where T is a non-trivial torus, and on the other the Kuznetsov trace…

For the group G = PGL(2) we prove nonstandard matching and the fundamental lemma between two relative trace formulas: on one hand, the relative trace formula of Jacquet for the quotient T\G/T, where T is a nontrivial torus; on the other,…

We elaborate an explicit version of the relative trace formula on $\PGL(2)$ over a totally real number field for the toral periods of Hilbert cusp forms along the diagonal split torus. As an application, we prove (i) a spectral…

We introduce a twisted relative trace formula which simultaneously generalizes the twisted trace formula of Langlands et.al. (in the quadratic case) and the relative trace formula of Jacquet and Lai. Certain matching statements relating…

We set up a trace formula for the relativistic density of states in terms of a topological sum of classical periodic orbits. The result is applicable to any relativistic integrable system.

We present a conceptual and uniform interpretation of the methods of integral representations of L-functions (period integrals, Rankin-Selberg integrals). This leads to: (i) a way to classify of such integrals, based on the classification…

In this paper, we will determine the factorization of global period attached to the spherical variety $X:=\mathrm{SO}(n-1)\backslash \mathrm{SO}(n)$, which is a special case of the Sakellaridis-Venkatesh conjecture. The main idea is to…

According to the Langlands functoriality conjecture, broadened to the setting of spherical varieties (of which reductive groups are special cases), a map between L-groups of spherical varieties should give rise to a functorial transfer of…

The relative Langlands program introduced by Ben-Zvi--Sakellaridis--Venkatesh posits a duality structure exchanging automorphic periods and L-functions, which can be encoded by pairs of dual Hamiltonian actions. In work of the author and…