Geodesic
New Estimates of the Remainder in an Asymptotic Formula in the Multidimensional Dirichlet Divisor Problem
Matematičeskie zametki, Tome 89 (2011) no. 4, pp. 530-546

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We obtain a new value of the Karatsuba constant in the multidimensional Dirichlet divisor problem. We also find a new value of the exponent of the main parameter in the estimate of the mean value of the remainder in a given asymptotics. The proof of the main statements is based on the derivation of a new estimate of the Carleson abscissa in the theory of the Riemann zeta function.
Keywords: Dirichlet divisor problem, Riemann zeta function, Carleson exponent, Dirichlet series.
Mots-clés : Karatsuba constant 
@article{MZM_2011_89_4_a5,
     author = {O. V. Kolpakova},
     title = {New {Estimates} of the {Remainder} in an {Asymptotic} {Formula} in the {Multidimensional} {Dirichlet} {Divisor} {Problem}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {530--546},
     publisher = {mathdoc},
     volume = {89},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_89_4_a5/}
}
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O. V. Kolpakova. New Estimates of the Remainder in an Asymptotic Formula in the Multidimensional Dirichlet Divisor Problem. Matematičeskie zametki, Tome 89 (2011) no. 4, pp. 530-546. http://geodesic.mathdoc.fr/item/MZM_2011_89_4_a5/