Research Directions in Number Theory by Unknown

Author:Unknown
Language: eng
Format: epub
ISBN: 9783030194789
Publisher: Springer International Publishing

Proposition 3.11

Let f(t) be an antiderivative of α or β, let m f < p − 2, and let k be the minimal valuation of the coefficients of f(pt). Fix an integer N such that m f + 2 ≤ N ≤ p p − p. Let ap e be the smallest integer greater than or equal to N with and e ≥ 1, and set

Then each simple root of p −k f M(pt) in equals the approximation modulo p ⌊(N−k)∕2⌋ of a root of f(pt). Furthermore, if all such roots are simple, then these are all the roots of f(pt) in .

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