Co-periods and central symmetric cube L-values

2025/07/21 by Cai, Li, Fan, Yangyu, She, Dongming
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2507.15279

Abstract

In this article, we study the co-period integral attached to an automorphic form on \GL(2) and two exceptional theta series on the cubic Kazhdan-Patterson cover of \GL(2). In the local aspect, we show the \Hom-space is always of one dimension and conduct the unramified calculations. In the global aspect, we give the Euler decomposition for the co-period integrals of Eisenstein series and propose an Ichino-Ikeda type conjecture relating the co-period integrals of cuspidal forms to the central critical value of symmetric cube L-functions. We also deduce from the local multiplicity one result that there exist cuspidal automorphic forms with prescribed local components and non-vanishing central symmetric cube L-values.

Citations

• Relative Langlands Duality
• Non-vanishing of symmetric cube L-functions
• Homological duality for covering groups of reductive p-adic groups
• Symmetric power functoriality for holomorphic modular forms
• Hida families and p-adic triple product L-functions
• Restriction of representations of metaplectic GL₂(F) to tori
• The characterization of theta-distinguished representations of GL_n
• Ext-analogues of Branching laws
• Periods and harmonic analysis on spherical varieties
• Bessel models for GSp(4)
• Relating invariant linear form and local epsilon factors via global methods

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• On certain period relations for cusp forms on GL_n
• Eisenstein series and the cubic moment for PGL(2)