An omega theorem on differences of two squares. II.
An Omega theorem on differences of two squares.
On sums of two kth powers: an asymptotic formula for the mean square of the error term
On sums of two cubes: an Ω₊-estimate for the error term
The arithmetic function 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 leads in a natural way to a certain error term which is known to be in mean-square. In this article it is proved that 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...
The Piltz divisor problem in number fields: An improved lower bound by Soundararajan's method
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