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On the 2 k -th power mean of L ' L ( 1 , χ ) with the weight of Gauss sums

Dongmei Ren, Yuan Yi (2009)

Czechoslovak Mathematical Journal

The main purpose of this paper is to study the hybrid mean value of L ' L ( 1 , χ ) and Gauss sums by using the estimates for trigonometric sums as well as the analytic method. An asymptotic formula for the hybrid mean value χ χ 0 | τ ( χ ) | | L ' L ( 1 , χ ) | 2 k of L ' L and Gauss sums will be proved using analytic methods and estimates for trigonometric sums.

On the distribution of ( k , r ) -integers in Piatetski-Shapiro sequences

Teerapat Srichan (2021)

Czechoslovak Mathematical Journal

A natural number n is said to be a ( k , r ) -integer if n = a k b , where k > r > 1 and b is not divisible by the r th power of any prime. We study the distribution of such ( k , r ) -integers in the Piatetski-Shapiro sequence { n c } with c > 1 . As a corollary, we also obtain similar results for semi- r -free integers.

On the distribution of p α modulo one

Xiaodong Cao, Wenguang Zhai (1999)

Journal de théorie des nombres de Bordeaux

In this paper, we give a new upper-bound for the discrepancy D ( N ) : = sup 0 γ 0 | p / N p α γ 1 - π ( N ) γ | for the sequence ( p α ) , when 5 / 3 α > 3 and α 2 .

Currently displaying 21 – 40 of 54