Vol. 89, No. 2, 1980

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Solution of the middle coefficient problem for certain classes of C-polynomials

Zalman Rubinstein

Vol. 89 (1980), No. 2, 431–437

A well-known conjecture states that for polynomials having all their zeros on the unit circle C half the maximum modulus on C bounds the modulus of all the coefficients. This has been established in all cases except for the middle coefficient of even degree polynomials greater than four. In this note this conjecture is verified for all even degree polynomials having simple zeros in a set of arcs dividing the circle into equal parts and related classes of polynomials. The local extremal polynomials are identified.

Mathematical Subject Classification 2000
Primary: 30C10
Received: 5 June 1979
Published: 1 August 1980
Zalman Rubinstein