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

Ankit Rai, Gunja Sachdeva

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