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11.
T. Zaimi 《Acta Mathematica Hungarica》2002,96(4):309-325
Let 1<q<2 be a real number, m≥1 be a rational integer and lm(q)={|P(q)|,P∈Z[X],P(q)≠0,H(P)≤m}, where Z[X] denotes the set of polynomials P with rational integer coefficients and H(P)
is the height of P. The value of lm(q) was determined for many particular Pisot numbers ([3] and [7]). In this paper we determine the infimum and the supremum
of the numbers lm(q) for any fixed m. We also determine the greatest limit point for the case m=1.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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Let K be a noncyclotomic CM field. We show that the field has a reciprocal unit-primitive element when K does. Also, we prove some related conditions that make the converse of this assertion true. 相似文献
14.
We count derangements, involutions and unimodal elements in the wreath product C
r
≀ S
n
by the numbers of excedances, fixed points and 2-cycles. Properties of the generating functions, including combinatorial
formulas, recurrence relations and real-rootedness are studied. The results obtained specialize to those on the symmetric
group S
n
and on the hyperoctahedral group B
n
when r = 1, 2, respectively. 相似文献
15.
Toufik Zaimi 《Archiv der Mathematik》2006,87(2):124-128
Let N be a positive rational integer and let P be the set of powers of a Salem number of degree d. We prove that for any α∈P the fractional parts of the numbers
, when n runs through the set of positive rational integers, are dense in the unit interval if and only if N≦ 2d − 4. We also show that for any α∈P the integer parts of the numbers αn are divisible by N for infinitely many n if and only if N≦ 2d − 3.
Received: 27 April 2005 相似文献
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