Twists and generalized Zolotarev polynomials
نویسندگان
چکیده
منابع مشابه
Twists and Generalized Zolotarev Polynomials
In the previous article [3], the author investigated Diophantine equations of the form (∗) X − f(x)Y 2 = 1 and found that the set of the polynomial solutions of (∗) can be described in terms of the theory of twists and that of generalized Jacobian varieties. On the other hand, there are several articles ([1], [7]) which relate the solutions of (∗) with certain torsion points on the Jacobian var...
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The algebraic form of Zolotarev polynomials refraining from their parametric representation is introduced. A recursive algorithm providing the coefficients for a Zolotarev polynomial of an arbitrary order is obtained from a linear differential equation developed for this purpose. The corresponding narrow-band, notch and complementary pair FIR filters are optimal in Chebyshev sense. A recursion ...
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Explicit expressions for Zolotarev polynomials of degree up to four have been known for long time (compare [15, 20]). One approach to compute Zolotarev polynomials is by quantifier elimination with cylindrical algebraic decomposition. In [5] this is used for computing Zolotarev polynomials up to degree 5. Challenged by Collins and Kaltofen [10] this was extended later up to degree 12 in [12]. A...
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This report is an appendix to [2] providing two pieces of information in addition to the explicit computations of [2]. On the one hand we treat the problem of explicit construction of proper Zolotarev polynomials of higher degree using explicit expressions for proper Zolotarev polynomials of lower degree. In particular we show how Z6, as computed in [2], is related to Z2. Furthermore, we provid...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2002
ISSN: 0030-8730
DOI: 10.2140/pjm.2002.203.379