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An inequality for the modulus of a polynomial evaluated at the roots of unity
Author(s) -
SheilSmall T.
Publication year - 2008
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdn076
Subject(s) - mathematics , root of unity , properties of polynomial roots , polynomial , degree (music) , combinatorics , modulus , pure mathematics , mathematical analysis , geometry , matrix polynomial , physics , quantum mechanics , acoustics , quantum
It is shown that if P ( z ) is an analytic polynomial of degree n and if N is a natural number with N > n , thenmax | z | = 1 | P ( z ) | ⩽ N / ( N − n )max ω | P ( ω ) | , where ω runs through the N th roots of unity.