منابع مشابه
Recent Progress on the Dirichlet Divisor Problem and the Mean Square of the Riemann Zeta-function
Let ∆(x) and E(t) denote respectively the remainder terms in the Dirichlet divisor problem and the mean square formula for the Riemann zeta-function on the critical line. This article is a survey of recent developments on the research of these famous error terms in number theory. These include upper bounds, Ω-results, sign changes, moments and distribution, etc. A few open problems will also be...
متن کاملOn the Mean Square of the Zeta-function and the Divisor Problem
Let ∆(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 |ζ( 1 2 + it)|. If E∗(t) = E(t) − 2π∆∗(t/2π) with ∆∗(x) = −∆(x) + 2∆(2x) − 1 2 ∆(4x), then we obtain the asymptotic formula ∫ T 0 (E(t)) dt = T P3(logT ) +Oε(T ), where P3 is a polynomial of degree three in log T with positive leading coefficient. The expone...
متن کاملOn the Mean Square of the Riemann Zeta Function and the Divisor Problem
Let ∆(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 ∆(T ) and E(T ) are asymptotic integral transforms of each other. We then use this integral representation of ∆(T ) to give a new proof of a result of M. Jutila.
متن کاملOn the mean square of the divisor function in short intervals
We provide upper bounds for the mean square integral
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2014
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa164-2-7