Notes on the Distribution of Roots Modulo a Prime of a Polynomial V: Weyl’s Criterion

Yoshiyuki Kitaoka ()
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Yoshiyuki Kitaoka: Independent Researcher, Nagoya 468-0073, Aichi, Japan

Mathematics, 2025, vol. 13, issue 21, 1-23

Abstract: Let f ( x ) be a monic integral polynomial of degree n and p a prime number, for which f ( x ) is fully decomposable modulo p . Let r 1 , … , r n be the roots of f ( x ) mod p with 0 ≤ r 1 ≤ ⋯ ≤ r n < p . We have conjectured that the sequence of ( r 1 , … , r n ) / p is uniformly distributed in some sense. We provide a clear explanation of this and generalize the Weyl criterion.

Keywords: local root of a polynomial; uniform distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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