Low-Lying Zeros of $L$-functions of Ad\'elic Hilbert Modular Forms and
their Convolutions
Low-Lying Zeros of $L$-functions of Ad\'elic Hilbert Modular Forms and
their Convolutions
In this article, we study the density conjecture of Katz and Sarnak for $L$-functions of ad\'elic Hilbert modular forms and their convolutions. In particular, under the generalised Riemann hypothesis, we establish several instances supporting the conjecture and extending the works of Iwaniec-Luo-Sarnak and many others. For applications, we obtain an …