On the higher moments of the error term in the divisor problem

Aleksandar Ivić, Patrick Sargos

Let $\Delta (x)$ denote the error term in the Dirichlet divisor problem. Our main results are the asymptotic formulas $$ \int_1^X Δ^3(x){\rm d}x = BX^{7/4} + O_ε(X^{β+ε}) \qquad(B > 0) $…