Fekete polynomial
In mathematics, a Fekete polynomial is a polynomial
where is the Legendre symbol modulo some integer p > 1.
These polynomials were known in nineteenth-century studies of Dirichlet L-functions, and indeed to Peter Gustav Lejeune 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.
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