Critical values of L -functions of residual representations of GL 4

Key Points

• The aim is to establish rationality results for critical values of L-functions related to representations in the residual spectrum.
• Applied Jacquet-Langlands correspondence to describe partial L-functions
• Utilized ideas from Grobner and Raghuram for computation
• Calculated critical values as a Shalika period up to a rational multiple.
• Established rationality for critical values of L-functions
• Described partial L-functions through cuspidal automorphic representations
• Computed specific critical values using the Shalika period.