Algebraicity of ratios of special $L$-values for $\mathrm{GL}(n)$

Ankit Rai, Gunja Sachdeva

We prove, under certain assumptions, algebraicity of the ratio $L(m,\hat{I}\times \ddot{I}‡)/L(m,\hat{I}\times \ddot{I}{‡}^{\prime })$, where $\hat{I}$ is a cuspidal automorphic cohomological unitary representation of…