Related papers: Beyond Endoscopy for the relative trace formula II…

We continue generalizing Altu\u{g}'s work on $\mathsf{GL}_2$ over $\mathbb{Q}$ in the unramified setting for \emph{Beyond Endoscopy} to the ramified case where ramification occurs at $S=\{\infty,q_1,\dots,q_r\}$ with $2\in S$, after…

Following a scheme suggested by B. Feigon, we investigate a local relative trace formula in the situation of a reductive $p$ -adic group $G$ relative to a symmetric subgroup $H= \underline{H}(F)$ where $\underline{H}$ is split over the…

In this article, we develop an arithmetic analogue of Fourier--Jacobi period integrals for a pair of unitary groups of equal rank. We construct the so-called Fourier--Jacobi cycles, which are algebraic cycles on the product of unitary…

We provide a uniform estimate for the $L^1$-norm (over any interval of bounded length) of the logarithmic derivatives of global normalizing factors associated to intertwining operators for the following reductive groups over number fields:…

By applying the new supersymmetric localization principle introduced in \cite{Choi:2021yuz,Choi:2023pjn}, we present two complementary approaches for the path integral derivation of the `non-chiral' trace formula for a semisimple compact…

We introduce a new class of symmetric space orbital integrals important for applications in certain relative trace formulas appearing in the theory of automorphic representations. We verify a fundamental lemma for $U_2\times…

It is shown that the pairing of the K00 group of a C*-algebra with the densely defined traces of the algebra can be extended to a pairing with the densely defined weights. For traces the pairing can be extended to the K0 group without the…

We establish an infinitesimal version of the Jacquet-Rallis trace formula for general linear groups. Our formula is obtained by integrating a kernel truncated a la Arthur multiplied by the absolute value of the determinant to the power $s…

At the beginning of this century, Langlands introduced a strategy known as \emph{Beyond Endoscopy} to attack the principle of functoriality. Altu\u{g} studied $\mathsf{GL}_2$ over $\mathbb{Q}$ in the unramified setting. The first step…

The main object considered in this paper is the trace function, defined as a suitably normalized trace of a product of intertwining operators for the Drinfeld-Jimbo quantum group, multiplied by the exponential of an element of the Cartan…

A natural generalization of Krein's theorem to a pair of commuting tuples $\left(H_1^0,H_2^0\right)$ and $\left(H_1,H_2\right)$ of bounded self-adjoint operators in a separable Hilbert space $\mathcal{H}$ with $H_j-H_j^0 = V_j\in…

We give a new, simple proof of the trace formula for Hecke operators on modular forms for finite index subgroups of the modular group. The proof uses algebraic properties of certain universal Hecke operators acting on period polynomials of…

In this paper we establish a coarse Jacquet-Zagier trace identity for GL$(n).$ We prove the absolute convergence when $\Re(s)>1$ and $0<\Re(s)<1;$ and obtain holomorphic continuation under almost all character twist. Moreover, as an…

We show that the cuspidal component of the stable trace formula of a special odd orthogonal group over a number field, satisfies a weak form of beyond endoscopic decomposition. We also study the $r$-stable trace formula, when $r$ is the…

Let G be a reductive algebraic group over Q, and suppose that Gamma is an arithmetic subgroup of G(R) defined by congruence conditions. A basic problem in arithmetic is to determine the multiplicities of discrete series representations in…

Let $E/F$ be a quadratic extension of number fields. We introduce truncated geometric and spectral RTF distributions associated to a Galois symmetric pair $G \subset \mathrm{Res}_{E/F} G_E$, subject to the constraint that $G$ and…

Through combining the work of Jean-Loup Waldspurger (\cite{waldspurger10} and \cite{waldspurgertemperedggp}) and Rapha\"el Beuzart-Plessis (\cite{beuzart2015local}), we give a proof for the tempered part of the local Gan-Gross-Prasad…

Let $E/F$ be an extension of number fields with $\mathrm{Gal}(E/F)$ simple and nonabelian. In [G] the first named author suggested an approach to nonsolvable base change and descent of automorphic representations of $\mathrm{GL}_2$ along…

In this paper, we prove, following earlier work of Waldspurger ([Wa1], [Wa4]), a sort of local relative trace formula which is related to the local Gan-Gross-Prasad conjecture for unitary groups over a local field $F$ of characteristic…

We derive a Gutzwiller-type trace formula for quantum chaotic systems that accounts for both particle spin precession and discrete geometrical symmetries. This formula generalises previous results that were obtained either for systems with…