Abstract
We show that in a family of L-functions, Hecke eigenvalues at a fixed prime are not too small and not too large except for a density zero set. The proof uses an effective form of the vertical Sato-Tate theorem.
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We thank the referee who read our paper carefully and gave many helpful remarks.
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Kim, H.H. Vertical Atkin-Serre conjecture and extremal primes in a family of L-functions. Res. number theory 10, 43 (2024). https://doi.org/10.1007/s40993-024-00529-2
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DOI: https://doi.org/10.1007/s40993-024-00529-2