A conjecture on Whittaker-Fourier coefficients of cusp forms

Abstract

We formulate an analogue of the Ichino-Ikeda conjectures for the Whittaker-Fourier coefficients of automorphic forms on quasi-split reductive groups. This sharpens the conjectures of Sakellaridis-Venkatesh in the case at hand.

Fixed small inaccuracies from prior version

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• Large values of cusp forms on GL(n)
• Whittaker rational structures and special values of the Asai $L$-function
• The double cover of odd general spin groups, small representations and applications
• Beyond Endoscopy for the relative trace formula II: global theory
• Bessel functions and local converse conjecture of Jacquet
• On Whittaker--Fourier coefficients of automorphic forms on unitary groups: reduction to a local identity
• A proof of the refined Gan--Gross--Prasad conjecture for non-endoscopic Yoshida lifts
• Cohomological representations for real reductive groups
• On Petersson norms of generic cusp forms and special values of adjoint $L$-functions for ${\mathrm{GSp}}_4$
• Theta distinguished representations, inflation and the symmetric square L-function
• Plancherel formula for ${\mathrm{GL}}_n(F)\backslash {\mathrm{GL}}_n(E)$ and applications to the Ichino-Ikeda and formal degree conjectures for unitary groups
• Multiplicities and Plancherel formula for the space of nondegenerate Hermitian matrices
• Galois representations for even general special orthogonal groups
• On a certain local identity for Lapid-Mao's conjecture and formal degree conjecture : even unitary group case
• The sup-norm problem beyond the newform
• Spectral average of central values of automorphic L-functions for holomorphic cusp forms on SO_0(m,2) II
• On the global Gan-Gross-Prasad conjecture for general spin groups
• On the Waldspurger Formula and the Metaplectic Ramanujan Conjecture over Number Fields
• Special values of $L$-functions and the refined Gan-Gross-Prasad conjecture
• Periods and global invariants of automorphic representations
• Acceptable compact Lie groups
• On the Gan-Gross-Prasad conjecture and its refinement for $\left(\mathrm{U}\left(2n\right),\mathrm{U}\left(1\right)\right)$
• Strongly tempered hyperspherical Hamiltonian spaces
• Hecke-Maass cusp forms on PGL_n of large levels with non-vanishing L-values
• Contragredient representations over local fields of positive characteristic