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Powers of cyclotomic integers and difference sets
Authors:Veikko Ennola
Institution:Department of Mathematics, University of Turku, Turku, Finland
Abstract:Let p be an odd prime, ζ = rxp(2πip), D a difference set mod p having a nontrivial multiplier, and ν = H(ζ), where H(x) is the Hall polynomial of D. For any α = Σi=0p?1aiζi with rational ai denote δ(α) = max ∥ ai ? aj ∥. Assuming that there are no nontrivial multiplicative dependence relations among the conjugates of ν, we obtain results for
/></figure>. We then show that for most known families of difference sets mod <em>p</em> the required independence result is valid. A conjecture concerning the exact value of the first number is stated. The conjecture is confirmed in certain particular cases.</td>
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