There has been a clear decline in the volume of oxygen in Earth's atmosphere over the past
20 years. Although the magnitude of this decrease appears small compared to the amount of …

In this article, we improve our main results from [LL21] in two directions: First, we allow
ramified places in the CM extension at which we consider representations that are spherical …

Abstract We establish the Fourier–Jacobi case of the local Gross–Prasad conjecture for
unitary groups, by using local theta correspondence to relate the Fourier–Jacobi case with …

In this paper, we prove the Gan-Gross-Prasad conjecture and the Ichino-Ikeda conjecture for
unitary groups U n× U n+ 1 in all the endoscopic cases. Our main technical innovation is the …

This paper generalizes the Gan–Gross–Prasad (GGP) conjectures that were earlier
formulated for tempered or more generally generic L-packets to Arthur packets, especially …

We introduce a new technique for isolating components on the spectral side of the trace
formula. By applying it to the Jacquet--Rallis relative trace formula, we complete the proof of …

In this article, we study the Beilinson–Bloch–Kato conjecture for motives associated to
Rankin–Selberg products of conjugate self-dual automorphic representations, within the …

The Local Langlands Conjecture for 𝑮2 Page 1 Forum of Mathematics, Pi (2023), Vol. 11:e28
1–42 doi:10.1017/fmp.2023.27 RESEARCH ARTICLE The Local Langlands Conjecture for 𝑮2 …

We express the Frobenius-Hecke traces on the compactly supported cohomology of a
Shimura variety of abelian type in terms of elliptic parts of stable Arthur-Selberg trace …

On the Gross–Prasad conjecture with its refinement for (SO(5), SO(2)) and the generalized
Böcherer conjecture Page 1 On the Gross–Prasad conjecture with its refinement for (SO(5) …