On an unconditional spectral analog of Selberg's result on S(t)

2024/10/04 by Sun, Qingfeng, Wang, Hui
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2410.03473

Abstract

Let S_j(t)=\frac1πarg L(1/2+it, u_j), where u_j is an even Hecke--Maass cusp form for \rm SL₂(ℤ) with Laplacian eigenvalue λ_j=(1)/(4)+t_j². Without assuming the GRH, we establish an asymptotic formula for the moments of S_j(t).

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