Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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SIMPLE ZEROS OF L-FUNCTIONS AND THE WEYL-TYPE SUBCONVEXITY

  • Peter Jaehyun Cho (Department of Mathematical Sciences Ulsan National Institute of Science and Technology) ;
  • Gyeongwon Oh (Department of Mathematical Sciences Ulsan National Institute of Science and Technology)
  • Received : 2022.05.18
  • Accepted : 2022.09.26
  • Published : 2023.01.01
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Abstract

Let f be a self-dual primitive Maass or modular forms for level 4. For such a form f, we define Nsf(T):=|{ρ ∈ ℂ : |𝕵(ρ)| ≤ T, ρ is a non-trivial simple zero of Lf(s)}|.. We establish an omega result for Nsf(T), which is $N^s_f(T) = \Omega(T^{\frac{1}{6}-{\epsilon}})$ for any ∊ > 0. For this purpose, we need to establish the Weyl-type subconvexity for L-functions attached to primitive Maass forms by following a recent work of Aggarwal, Holowinsky, Lin, and Qi.

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Acknowledgement

We thank the anonymous referee who carefully read our poorly written manuscript and gave many valuable comments.

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