The paper shows that critical values of L-functions for residual representations of GL_4 are rational multiples of Shalika periods, obtained by transferring to cuspidal representations on GL_2 over a quaternion algebra.
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Critical values of $L$-functions of residual representations of $\mathrm{GL}_4$
The paper shows that critical values of L-functions for residual representations of GL_4 are rational multiples of Shalika periods, obtained by transferring to cuspidal representations on GL_2 over a quaternion algebra.