On the method of exponent pairs
Let Δ(x) denote the error term in the Dirichlet divisor problem, and E(T) the error term in the asymptotic formula for the mean square of . If with , then we obtain . We also show how our method of proof yields the bound , where T 1/5+ε≤G≪T, T
Let Δ(x) denote the error term in the Dirichlet divisor problem, and E(T) the error term in the asymptotic formula for the mean square of . If E *(t)=E(t)-2πΔ*(t/2π) with , then we obtain and It is also shown how bounds for moments of | E *(t)| lead to bounds for moments of .