Zeros of Fekete polynomials

An extremal property of Fekete polynomials

“…This and further properties of Fekete polynomials, including the behavior of their zeros, are discussed in [6].…”

On the zeros of cosine polynomials: solution to a problem of Littlewood

“…See [9], [10], and [11], and in particular Littlewood's delightful monograph [12]. Related problems and results may be found in [2] and [4], for example. One of these is Littlewood's well-known conjecture of around 1948 asking for the minimum L 1 norm of polynomials of the form…”

Untitled

“…In a private communication, B. Conrey asked how fast the number of zeros of the above sums in a period tends to ∞ as a function of N . In [43], the authors observed that for an odd prime p the Fekete polynomial f p (z) = Here the real zeros are counted in a period. In fact no progress appears to have been made on this in the last half century.…”