On the zeros of certain polynomials
نویسندگان
چکیده
منابع مشابه
The Zeros of Certain Composite Polynomials
we may obtain various theorems on the relative location of the zeros of A 0(2) and An(z) by the familiar method of first finding such relations for two successive Ak{z) and then iterating the relations n times. This method has already been employed in the study of the zeros of sequence (1.1) for the following three cases: (1) for all k, Pk = 0 and yk is real; 1 (2) for all k, yk~m + l—a limitin...
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Abstract. We extend Aziz and Mohammad’s result that the zeros, of a polynomial P (z) = ∑n j=0 ajz , taj > aj−1 > 0, j = 2, 3, . . . , n for certain t ( > 0), with moduli greater than t(n − 1)/n are simple, to polynomials with complex coefficients. Then we improve their result that the polynomial P (z), of degree n, with complex coefficients, does not vanish in the disc |z − ae| < a/(2n); a > 0,...
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Using techinques of complex dynamics we prove the conjecture of Sheil-Small and Wilmshurst that the harmonic polynomial z − p(z), deg p = n > 1, has at most 3n− 2 complex zeros.
متن کاملOn the Zeros of Certain Poincaré Series
We locate all of the zeros of certain Poincaré series associated with the Fricke groups Γ0(2) and Γ ∗ 0(3) in their fundamental domains by applying and extending the method of F. K. C. Rankin and H. P. F. Swinnerton-Dyer (“On the zeros of Eisenstein series”, 1970).
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We locate all of the zeros of certain Poincaré series associated with the Fricke groups Γ0(2) and Γ ∗ 0(3) in their fundamental domains by applying and extending the method of F. K. C. Rankin and H. P. F. Swinnerton-Dyer (“On the zeros of Eisenstein series”, 1970).
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2002
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-02-06454-7