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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. ==References== * Peter Borwein: ''Computational excursions in analysis and number theory.'' Springer, 2002, ISBN 0-387-95444-9, Chap.5. 抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Fekete polynomial」の詳細全文を読む スポンサード リンク
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