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Algebraic points of small height with additional arithmetic conditionsFukshansky, Leonid Eugene 28 August 2008 (has links)
Not available / text
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Mahler measure evaluations in terms of polylogarithmsCondon, John Donald 28 August 2008 (has links)
Not available / text
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Multiplicative distance functionsSinclair, Christopher Dean 28 August 2008 (has links)
Not available / text
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Auxiliary polynomials and height functionsSamuels, Charles Lloyd, 1980- 28 August 2008 (has links)
We establish two new results in this dissertation. Recent theorems of Dubickas and Mossinghoff use auxiliary polynomials to give lower bounds on the Weil height of an algebraic number [alpha] under certain assumptions on [alpha]. We prove a theorem which introduces an auxiliary polynomial for giving lower bounds on the height of any algebraic number. In particular, we prove the following theorem. [Mathematical equations] / text
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POLYNOMIALS WITH SMALL VALUE SET OVER FINITE FIELDS.GOMEZ-CALDERON, JAVIER. January 1986 (has links)
Let K(q) be the finite field with q elements and characteristic p. Let f(x) be a monic polynomial of degree d with coefficients in K(q). Let C(f) denote the number of distinct values of f(x) as x ranges over K(q). It is easy to show that C(f) ≤ [|(q - 1)/d|] + 1. Now, there is a characterization of polynomials of degree d < √q for which C(f) = [|(q - 1)/d|] +1. The main object of this work is to give a characterization for polynomials of degree d < ⁴√q for which C(f) < 2q/d. Using two well known theorems: Hurwitz genus formula and Andre Weil's theorem, the Riemann Hypothesis for Algebraic Function Fields, it is shown that if d < ⁴√q and C(f) < 2q/d then f(x) - f(y) factors into at least d/2 absolutely irreducible factors and f(x) has one of the following forms: (UNFORMATTED TABLE FOLLOWS) f(x - λ) = D(d,a)(x) + c, d|(q² - 1), f(x - λ) = D(r,a)(∙ ∙ ∙ ((x²+b₁)²+b₂)²+ ∙ ∙ ∙ +b(m)), d|(q² - 1), d=2ᵐ∙r, and (2,r) = 1 f(x - λ) = (x² + a)ᵈ/² + b, d/2|(q - 1), f(x - λ) = (∙ ∙ ∙((x²+b₁)²+b₂)² + ∙ ∙ ∙ +b(m))ʳ+c, d|(q - 1), d=2ᵐ∙r, f(x - λ) = xᵈ + a, d|(q - 1), f(x - λ) = x(x³ + ax + b) + c, f(x - λ) = x(x³ + ax + b) (x² + a) + e, f(x - λ) = D₃,ₐ(x² + c), c² ≠ 4a, f(x - λ) = (x³ + a)ⁱ + b, i = 1, 2, 3, or 4, f(x - λ) = x³(x³ + a)³ +b, f(x - λ) = x⁴(x⁴ + a)² +b or f(x - λ) = (x⁴ + a) ⁱ + b, i = 1,2 or 3, where D(d,a)(x) denotes the Dickson’s polynomial of degree d. Finally to show other polynomials with small value set, the following equation is obtained C((fᵐ + b)ⁿ) = αq/d + O(√q) where α = (1 – (1 – 1/m)ⁿ)m and the constant implied in O(√q) is independent of q.
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A study of polynomials, determinants, eigenvalues and numerical rangesover real quaternions邵樂遜, Siu, Lok-shun. January 1997 (has links)
published_or_final_version / Mathematics / Master / Master of Philosophy
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On p-adic polynomials and power seriesChan, Man-fai, 陳文輝 January 2000 (has links)
published_or_final_version / Mathematics / Master / Master of Philosophy
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Images of linear coordinates in polynomial algebras of rank two陳晨代, Chan, San-toi. January 2001 (has links)
published_or_final_version / Mathematics / Master / Master of Philosophy
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A solution for the general polynomial by an analog techniqueSchweppe, Fred C. January 1956 (has links)
No description available.
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An analog method for the root solution of algebraic polynomialsSmith, Jack, 1927- January 1958 (has links)
No description available.
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