Displaying similar documents to “Counting irreducible polynomials over finite fields”

On the mean value of the generalized Dirichlet L -functions

Rong Ma, Yuan Yi, Yulong Zhang (2010)

Czechoslovak Mathematical Journal

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Let q ≥ 3 be an integer, let χ denote a Dirichlet character modulo q . For any real number a ≥ 0 we define the generalized Dirichlet L -functions L ( s , χ , a ) = ∑ n = 1 ∞ χ ( n ) ( n + a ) s , where s = σ + i t with σ > 1 and t both real. They can be extended to all s by analytic continuation. In this paper we study the mean value properties of the generalized Dirichlet L -functions especially for s = 1 and s = 1 2 + i t , and obtain two sharp asymptotic formulas by using the analytic method and the theory of van der Corput.

On the Euler function of repdigits

Florian Luca (2008)

Czechoslovak Mathematical Journal

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For a positive integer n we write φ ( n ) for the Euler function of n . In this note, we show that if b > 1 is a fixed positive integer, then the equation φ x b n - 1 b - 1 = y b m - 1 b - 1 , where x , y ∈ { 1 , ... , b - 1 } , has only finitely many positive integer solutions ( x , y , m , n ) .