4 citations · 5 across the 3 of their papers we have counts for
4 papers · 1 filter
On some mean value results for the zeta-function and a divisor problem II
Aleksandar Ivić, Wenguang Zhai
Let be the number of divisors of , let denote Euler's constant and denote the error term in the classical Dirichlet…
Higher moments of the error term in the divisor problem
Aleksandar Ivić, Wenguang Zhai
It is proved that, if is a fixed integer and , then $$ \int_{X-H}^{X+H}Δ^4_k(x)\d x \ll_εX^ε\Bigl(HX^{(2k-2)/k} + H^{(2k-3)/(2k+1)}X^{(8k-8)/(2k+1)}\Bigr),…
On the mean square of the divisor function in short intervals
Aleksandar Ivić
We provide upper bounds for the mean square integral $$ \int_X^{2X}(Δ_k(x+h) - Δ_k(x))^2 dx \qquad(h = h(X)\gg1, h = o(x) {\roman{as}} X\to\infty) $$ where lies in a suitable r…
On the higher moments of the error term in the divisor problem
Aleksandar Ivić, Patrick Sargos
Let denote the error term in the Dirichlet divisor problem. Our main results are the asymptotic formulas $$ \int_1^X Δ^3(x){\rm d}x = BX^{7/4} + O_ε(X^{β+ε}) \qquad(B > 0) $…