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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

Some numerical results on Fekete polynomials


Authors: Paul T. Bateman, George B. Purdy and Samuel S. Wagstaff
Journal: Math. Comp. 29 (1975), 7-23
MSC: Primary 10-04; Secondary 10H10
MathSciNet review: 0480293
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Abstract | References | Similar Articles | Additional Information

Abstract: It is known that if $ \chi $ is a real residue character modulo k with $ \chi (p) = - 1$ for the first five primes p, then the corresponding Fekete polynomial $ \Sigma _{n = 1}^k\;\chi (n){x^n}$ changes sign on (0, 1). In this paper it is shown that the condition that $ \chi (p)$ be -1 for the first four primes p is not sufficient to guarantee such a sign change. More specifically, if $ \chi $ is the real nonprincipal character modulo either 1277 or 1973, it is shown that the corresponding Fekete polynomial is positive throughout (0, 1) even though $ \chi (2) = \chi (3) = \chi (5) = \chi (7) = - 1$.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1975-0480293-9
PII: S 0025-5718(1975)0480293-9
Keywords: Real residue characters, Chowla's method, Dirichlet L-functions, Fekete polynomials, real zeros of polynomials
Article copyright: © Copyright 1975 American Mathematical Society