Estimates of convolutions of certain number-theoretic error terms

Aleksandar Ivic

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-23

Abstract:

Several estimates for the convolution function C   [ f ( x ) ] : = ∫ 1 x f ( y )   f ( x / y ) ( d y / y ) and its iterates are obtained when f ( x ) is a suitable number-theoretic error term. We deal with the case of the asymptotic formula for ∫ 0 T | ζ ( 1 / 2 + i t ) | 2 k d t ( k = 1 , 2 ) , the general Dirichlet divisor problem, the problem of nonisomorphic Abelian groups of given order, and the Rankin-Selberg convolution.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:317515

DOI: 10.1155/S0161171204305156

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