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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

13 votes
3 answers
982 views

linear independence of $\sin(k \pi / m)$

I have tried searching the literature for a result like the following, but have not found anything. For a positive integer $m$, is it known that $$\{ \sin (k \pi / m): 1 \leq k \leq m/2, (k,m)=1 \}$$ …