Fekete polynomial

In mathematics, a Fekete polynomial is a polynomial
where formula_2 is the Legendre symbol modulo some integer "p" > 1.
These polynomials were known in nineteenth-century studies of Dirichlet L-functions, and indeed to Dirichlet himself. They have acquired the name of Michael Fekete, who observed that the absence of real zeroes "t" of the Fekete polynomial with 0 < "t" < 1 implies an absence of the same kind for the L-function
This is of considerable potential interest in number theory, in connection with the hypothetical Siegel zero near "s" = 1. While numerical results for small cases had indicated that there were few such real zeroes, further analysis reveals that this may indeed be a 'small number' effect.