caa a22 4500 463178106 CHVBK 20180406164831.0 cr unu---uuuuu 170326e20071001xx s 000 0 eng 10.1007/s11139-007-9029-5 doi (NATIONALLICENCE)springer-10.1007/s11139-007-9029-5 Self-inversive polynomials of odd degree [Elektronische Daten] [László Losonczi, Andrzej Schinzel] If the coefficients of a self-inversive polynomial P(z)=∑ k=0 m A k z k ∈ℂ[z] of odd degree m≥3 satisfy the inequality $$|A_{m}|\ge \cos \frac{\pi }{2(m+1)}\inf_{\scriptstyle{c,d\in\mathbb{C}}\atop\scriptstyle{|d|=1}}\sum _{k=0}^{m}|cA_{k}-d^{m-k}A_{m}|,$$ then all zeros of P are on the unit circle and they are simple. This is an improvement of a recent result of the second author (Ramanujan J. 9, 19-23, 2005) on the zeros of self-inversive polynomials in the case of polynomials of odd degree. A similar improvement in the case of real (reciprocal) polynomials has been given by Lakatos and the first author(J. Inequal. Pure Appl. Math. 4(3), 2003). Springer Science+Business Media, LLC, 2007 Self-inversive polynomials nationallicence Zeros nationallicence Losonczi László Faculty of Economics and Business Administration, University of Debrecen, Kassai u. 26, 4028, Debrecen, Hungary aut Schinzel Andrzej Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland aut The Ramanujan Journal Springer US; http://www.springer-ny.com 14/2(2007-10-01), 305-320 1382-4090 14:2<305 2007 14 11139 https://doi.org/10.1007/s11139-007-9029-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11139-007-9029-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Losonczi László Faculty of Economics and Business Administration, University of Debrecen, Kassai u. 26, 4028, Debrecen, Hungary aut NATIONALLICENCE 700 1- Schinzel Andrzej Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland aut NATIONALLICENCE 773 0- The Ramanujan Journal Springer US; http://www.springer-ny.com 14/2(2007-10-01), 305-320 1382-4090 14:2<305 2007 14 11139 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer