简介:LetKbeanalgebraicnumberfieldoffinitedegreeovertherationalfieldQ,andaK(n)thenumberofintegralidealsinKwithnormn.WhenKisaGaloisextensionoverQ,manyauthorscontributetotheintegralpowersumsofaK(n),Σn≤xaK(n)l,l=1,2,3,···.Thispaperisinterestedinthedistributionofintegralidealsconcerningdifferentnumberfields.TheauthorisabletoestablishasymptoticformulaefortheconvolutionsumΣn≤xaK1(nj)laK2(nj)l,j=1,2,l=2,3,···,whereK1andK2aretwodifferentquadraticfields.