Displaying similar documents to “On the 2 k -th power mean of L ' L ( 1 , χ ) with the weight of Gauss sums”

A hybrid mean value of the Dedekind sums

Hai Yang (2010)

Czechoslovak Mathematical Journal

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The main purpose of this paper is to use the M. Toyoizumi's important work, the properties of the Dedekind sums and the estimates for character sums to study a hybrid mean value of the Dedekind sums, and give a sharper asymptotic formula for it.

A hybrid mean value involving two-term exponential sums and polynomial character sums

Han Di (2014)

Czechoslovak Mathematical Journal

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Let q ≥ 3 be a positive integer. For any integers m and n , the two-term exponential sum C ( m , n , k ; q ) is defined by C ( m , n , k ; q ) = ∑ a = 1 q e ( ( m a k + n a ) / q ) , where e ( y ) = e 2 π i y . In this paper, we use the properties of Gauss sums and the estimate for Dirichlet character of polynomials to study the mean value problem involving two-term exponential sums and Dirichlet character of polynomials, and give an interesting asymptotic formula for it.

Second moments of Dirichlet L -functions weighted by Kloosterman sums

Tingting Wang (2012)

Czechoslovak Mathematical Journal

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For the general modulo q ≥ 3 and a general multiplicative character χ modulo q , the upper bound estimate of | S ( m , n , 1 , χ , q ) | is a very complex and difficult problem. In most cases, the Weil type bound for | S ( m , n , 1 , χ , q ) | is valid, but there are some counterexamples. Although the value distribution of | S ( m , n , 1 , χ , q ) | is very complicated, it also exhibits many good distribution properties in some number theory problems. The main purpose of this paper is using the estimate for k -th Kloosterman sums and analytic method to study the asymptotic...