| Title |
Cosine polynomials with few zeros |
| Authors |
JuΕ‘keviΔius, Tomas ; Sahasrabudhe, Julian |
| DOI |
10.1112/blms.12468 |
| Full Text |
|
| Is Part of |
Bulletin of the London Mathematical Society.. Hoboken : Wiley. 2021, vol. 53, iss. 3, p. 877-892.. ISSN 0024-6093. eISSN 1469-2120 |
| Keywords [eng] |
cosine polynomials ; old conjecture of Littlewood ; analysis of their constructions |
| Abstract [eng] |
In a celebrated paper, Borwein, ErdΓ©lyi, Ferguson and Lockhart constructed cosine polynomials of the form ππ΄(π₯)=βπβπ΄cos(ππ₯), with π΄ββ, |π΄|=π and as few as π5/6+π(1) zeros in [0,2π], thereby disproving an old conjecture of Littlewood. Here we give a sharp analysis of their constructions and, as a result, prove that there exist examples with as few as πΆ(πlogπ)2/3 zeros. |
| Published |
Hoboken : Wiley |
| Type |
Journal article |
| Language |
English |
| Publication date |
2021 |
| CC license |
|
