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

April 23, 2026

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.

Abstract

In this paper we prove rationality results for critical values for Formula: see text-functions attached to representations in the residual spectrum of Formula: see text. We use the Jacquet-Langlands correspondence to describe their partial Formula: see text-functions via cuspidal automorphic representations of the group Formula: see text over a quaternion algebra. Using ideas inspired by results of Grobner and Raghuram we are then able to compute the critical values as a Shalika period up to a rational multiple.

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Cite This Study

Johannes Droschl (Tue,) studied this question.

synapsesocial.com/papers/69e9b8d485696592c86ebecf https://doi.org/https://doi.org/10.1142/s1793042126500910