Currently displaying 1 – 3 of 3

Showing per page

Order by Relevance | Title | Year of publication

On sums of two cubes: an Ω₊-estimate for the error term

M. KühleitnerW. G. NowakJ. SchoissengeierT. D. Wooley — 1998

Acta Arithmetica

The arithmetic function r k ( n ) counts the number of ways to write a natural number n as a sum of two kth powers (k ≥ 2 fixed). The investigation of the asymptotic behaviour of the Dirichlet summatory function of r k ( n ) leads in a natural way to a certain error term P k ( t ) which is known to be O ( t 1 / 4 ) in mean-square. In this article it is proved that P ( t ) = Ω ( t 1 / 4 ( l o g l o g t ) 1 / 4 ) as t → ∞. Furthermore, it is shown that a similar result would be true for every fixed k > 3 provided that a certain set of algebraic numbers contains a sufficiently...

Page 1

Download Results (CSV)