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Least primitive roots modulo the square of a prime ideal
Published online by Cambridge University Press: 26 February 2010
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Let K be an algebraic number field of degree n = r1 + 2r2 (in the usual notation) over the rationals. ZK will denote the ring of integers in K. Consider the set of all totally positive primitive roots modulo the square of a prime ideal p of first degree in K. We recall (see e.g., [6], p. 249) that there exists such a primitive root mod p2, if, and only if, p is of first degree. Let vp be a least element of this set, least in the sense that its norm Nvp is minimal. We ask for the order of magnitude of Nvp in comparison to Np2. The author”s work [5] on cubefree ideal modulus character sums yields the estimate
for any a > 0, where the implied «-constant depends on a and K.
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- Research Article
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- Copyright © University College London 1986
References
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