We prove that the angles of Kloosterman sums over arbitrary finite field are incommensurable with the constant π. In particular, this implies that the Weil bound for Kloosterman sums over finite fields cannot be reached.
Research Article
Irrationality of the Angles of Kloosterman Sums over Finite Field
https://doi.org/10.21203/rs.3.rs-989563/v1
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We prove that the angles of Kloosterman sums over arbitrary finite field are incommensurable with the constant π. In particular, this implies that the Weil bound for Kloosterman sums over finite fields cannot be reached.
Kloosterman sum over finite field
angle of the Kloosterman sum
Weil bound.
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