Abstract
We study the argument of L(s, f) associated with holomorphic cusp form in both weight aspect and t-aspect. We prove that for −1 ≤ σ ≤ 2 and t ≥ 4, argL(s, f) ≪ log kt, where s = σ + it. Assuming the generalized Riemann hypothesis (GRH), we have arg L(s, f) ≪ log kt/log log kt for σ ≥ 1/2 and t ≥ 4.
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This work is supported by the Science and Technology Development Fund, Macau SAR (file No. 0095/2018/A3).
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Yang, Q. Estimates of the argument function of automorphic L-functions for GL(2)∗. Lith Math J 61, 106–122 (2021). https://doi.org/10.1007/s10986-021-09510-3
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DOI: https://doi.org/10.1007/s10986-021-09510-3