L⁴-norms and sign changes of Maass forms

2023/02/06 by Haseo Ki, Ki, Haseo · 2 citations
Mathematics · #11F30. Secondary: 35P20 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Primary: 11F12

paper · pdf · doi:10.48550/arxiv.2302.02625

openalex publication_date 2023/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Unconditionally, we prove the Iwaniec-Sarnak conjecture for L⁴-norms of the Hecke-Maass cusp forms. From this result, we can justify that for even Maass cusp form ϕ with the eigenvalue λ_ϕ=(1)/(4)+t_ϕ², for a>0, a sufficiently large h>0 and for any 0<ε₁<ε/10⁷ (ε>0) , for almost all 1≤ k0, the number of sign changes of ϕ along β is ≫_ε t_ϕ^1-ε and consequently, the number of inert nodal domains meeting any compact vertical segment on the imaginary axis is ≫_ε t_ϕ^1-ε as t_ϕ→∞.

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