Under GRH, the authors establish 1-level density asymptotics for Hilbert modular form L-functions and their Rankin-Selberg convolutions, with applications to average orders and non-vanishing.
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Low-Lying Zeros of $L$-functions of Ad\'elic Hilbert Modular Forms and their Convolutions
Under GRH, the authors establish 1-level density asymptotics for Hilbert modular form L-functions and their Rankin-Selberg convolutions, with applications to average orders and non-vanishing.