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On the mean square of the Riemann zeta function and the divisor problem. (English) Zbl 1247.11109

Summary: 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 in 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 [Ann. Univ. Turku., Ser. A I 186, 23–30 (1984; Zbl 0536.10032)].

MSC:

11M06 \(\zeta (s)\) and \(L(s, \chi)\)
11N37 Asymptotic results on arithmetic functions

Citations:

Zbl 0536.10032
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