On the Mean Square of the Riemann Zeta Function and the Divisor Problem
Publications de l'Institut Mathématique, _N_S_83 (2008) no. 97, p. 71
Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
Let $\Delta(T)$ and $E(T)$ be the error terms in the classical Dirichlet divisor problem
and in the asymptotic formula for the mean square of the Riemann zeta function
on the critical strip, respectively.
We show that $\Delta(T)$ and $E(T)$ are asymptotic integral transforms of each other.
We then use this integral representation of $\Delta(T)$ to give a new proof of a result of M. Jutila.
@article{10_2298_PIM0897071Y,
author = {Yifan Yang},
title = {On the {Mean} {Square} of the {Riemann} {Zeta} {Function} and the {Divisor} {Problem}},
journal = {Publications de l'Institut Math\'ematique},
pages = {71 },
publisher = {mathdoc},
volume = {_N_S_83},
number = {97},
year = {2008},
doi = {10.2298/PIM0897071Y},
zbl = {1247.11109},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM0897071Y/}
}
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Yifan Yang. On the Mean Square of the Riemann Zeta Function and the Divisor Problem. Publications de l'Institut Mathématique, _N_S_83 (2008) no. 97, p. 71 . doi: 10.2298/PIM0897071Y
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