Article
Statistical Relation of Roots of a Polynomial in Different Local Fields Iv
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Abstract
Let f(x) = xn+an−1xn−1+· · · be an irreducible polynomial with integer coefficients, and L a natural number. For a prime p for which f(x) mod p is completely decomposable, we consider the n roots ri with ri ≡ 0 mod L and 0 ≤ ri < pL. We propose several conjectures on the distribution of integers (an−1 + P ri)/p when p varies. We have studied the case L = 1 in previous papers, and this is a continuation.
Keywords
polynomial, roots modulo prime, distribution.
Citation
Kitaoka, Y. (2013). Statistical relation of roots of a polynomial in different local fields iv. Uniform Distribution Theory, 8(1), 17–30.
Y. Kitaoka, “Statistical relation of roots of a polynomial in different local fields iv,” Uniform Distribution Theory, vol. 8, no. 1, pp. 17–30, 2013.
Kitaoka Y. Statistical relation of roots of a polynomial in different local fields iv. Uniform Distribution Theory. 2013;8(1):17–30.
Kitaoka, Y. (2013), ‘Statistical relation of roots of a polynomial in different local fields iv’, Uniform Distribution Theory, 8(1), pp. 17–30.
Kitaoka, Yoshiyuki. “Statistical Relation of Roots of a Polynomial in Different Local Fields Iv.” Uniform Distribution Theory, vol. 8, no. 1, 2013, pp. 17–30.
Kitaoka, Yoshiyuki. “Statistical Relation of Roots of a Polynomial in Different Local Fields Iv.” Uniform Distribution Theory 8, no. 1 (2013): 17–30.
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Published by: Engineering Journals
