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If Z is a sum of t distinct roots of unity and |Z| is a rational integer, can someone find a bound on |Z| in terms of k=deg(Q(Z):Q))? Clearly we need to have distinct roots of unity otherwise this won't work! Correction: Let assume that Z is not rational itself otherwise obviously it's wrong. Here I hope to extend the proof of Kronecker thm! I have "Z is a sum of t distinct roots of unity and |Z| is a rational integer" I conjecture that either Z is rational or a root of unity! |
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is there any bound on the absolute number of algebraic integer in terms of its degree?If Z is a sum of t distinct roots of unity and |Z| is a rational integer, can someone find a bound on |Z| in terms of k=deg(Q(Z):Q))? Clearly we need to have distinct roots of unity otherwise this won't work!
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