Geodesic
On the approximation of π by special algebraic numbers
Glasgow mathematical journal, Tome 21 (1980) no. 1, pp. 51-56

Voir la notice de l'article provenant de la source Cambridge University Press

Suppose that m0 is an integer, m0≥3, ρ = exp(2πi/m0), K = Q(ρ, i), v denotes the degree of K, ξ∈K has degree N over Q. The length, where is the (irreducible) minimal polynomial for with ξ relatively prime integer coefficients. Feldman [2, p. 49] proved that there is an absolute constant c0>0 such thatFrom [2, p. 49, Notes 1 and 2] we know that v = φ(m0) or v = 2φ(m0), and φ(m0)≥ c1m0(log log m0)−1 (c1 > an absolute constant), where φ(m0) denotes Euler's function. 
Braune, Erhard. On the approximation of π by special algebraic numbers. Glasgow mathematical journal, Tome 21 (1980) no. 1, pp. 51-56. doi: 10.1017/S0017089500003979
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[1] 1.Cijsouw, P. L., A transcendence measure for π, Transcendence theory: advances and applications, Proc. of a conference in Cambridge 1976 (Ed. Baker, A. and Masser, D. W.), (Academic Press, 1977). Google Scholar

[2] 2.Feldman, N. I., Approximation of number π by algebraic numbers from special fields, J. Number Theory 9 (1977), 48–60. Google Scholar | DOI

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