Displaying similar documents to “The degree of the splitting field of a random polynomial over a finite field.”

Counting irreducible polynomials over finite fields

Qichun Wang, Haibin Kan (2010)

Czechoslovak Mathematical Journal

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In this paper we generalize the method used to prove the Prime Number Theorem to deal with finite fields, and prove the following theorem: π ( x ) = q q - 1 x log q x + q ( q - 1 ) 2 x log q 2 x + O x log q 3 x , x = q n → ∞ where π ( x ) denotes the number of monic irreducible polynomials in F q [ t ] with norm ≤ x .

Some subclasses of close-to-convex functions

Adam Lecko (1993)

Annales Polonici Mathematici

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For α ∈ [0,1] and β ∈ (-π/2,π/2) we introduce the classes C β ( α ) defined as follows: a function f regular in U = z: |z| < 1 of the form f ( z ) = z + ∑ n = 1 ∞ a n z n , z ∈ U, belongs to the class C β ( α ) if R e e i β ( 1 - α ² z ² ) f ' ( z ) < 0 for z ∈ U. Estimates of the coefficients, distortion theorems and other properties of functions in C β ( α ) are examined.