Happy new year to everybody. Ok, see if you like this problem as much as I do: Let and suppose that Prove that if then Source: Alex Lupas Note: The problem has a simple generalization.
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Originally Posted by NonCommAlg Happy new year to everybody. Ok, see if you like this problem as much as I do: Let and suppose that Prove that if then Source: Alex Lupas Note: The problem has a simple generalization. If we make a substitution , multiply by , and the estimate for the module, then the problem equivalent of this problem . This amount is considered to be easy, and with and it's equal to 1. I apologize if I don't quite understood the condition of your problem.
Originally Posted by DeMath If we make a substitution , multiply by , and the estimate for the module, then the problem equivalent of this problem . yes, proving the inequality will solve the problem!
Also we can not difficult to prove your problem by methods of complex analysis, using Rouche's theorem. P.S. I would be interested to see your proof.
in general: let and such that: suppose also that and: then all roots of lie in the disc to prove this, suppose that and first note that if then: now we have: therefore: but by and our assumption: contradiction!
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