Low-lying zero densities for Hecke-Maass L-functions over class-number-one imaginary quadratic fields match orthogonal random matrix ensembles in the level and eigenvalue aspects.
A Bessel delta-method and exponential sums for GL(2)
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abstract
In this paper, we introduce a simple Bessel $\delta$-method to the theory of exponential sums for $\rm GL_2$. Some results of Jutila on exponential sums are generalized in a less technical manner to holomorphic newforms of arbitrary level and nebentypus. In particular, this gives a short proof for the Weyl-type subconvex bound in the $t$-aspect for the associated $L$-functions.
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Low-lying zeros of $L$-functions for Maass forms over imaginary quadratic fields
Low-lying zero densities for Hecke-Maass L-functions over class-number-one imaginary quadratic fields match orthogonal random matrix ensembles in the level and eigenvalue aspects.