On the Mean Square of the Riemann Zeta Function and the Divisor Problem
Yifan Yang (2008)
Publications de l'Institut Mathématique
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Displaying similar documents to “On the Selberg Integral of the -divisor Function and the -th Moment of the Riemann Zeta-function”
On the Mean Square of the Riemann Zeta Function and the Divisor Problem
An integral involving the generalized zeta function.
Elizalde, E., Romeo, A. (1990)
International Journal of Mathematics and Mathematical Sciences
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Some problems on mean values of the Riemann zeta-function
Aleksandar Ivić (1996)
Journal de théorie des nombres de Bordeaux
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Several problems and results on mean values of are discussed. These include mean values of and the fourth moment of for .
On the riemann zeta-function and the divisor problem II
Aleksandar Ivić (2005)
Open Mathematics
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Let Δ(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 . If E *(t)=E(t)-2πΔ*(t/2π) with , then we obtain and It is also shown how bounds for moments of | E *(t)| lead to bounds for moments of .
On certain arithmetic functions involving the greatest common divisor
Ekkehard Krätzel, Werner Nowak, László Tóth (2012)
Open Mathematics
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The paper deals with asymptotics for a class of arithmetic functions which describe the value distribution of the greatest-common-divisor function. Typically, they are generated by a Dirichlet series whose analytic behavior is determined by the factor ζ2(s)ζ(2s − 1). Furthermore, multivariate generalizations are considered.
On a question of A. Schinzel: Omega estimates for a special type of arithmetic functions
Manfred Kühleitner, Werner Nowak (2013)
Open Mathematics
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The paper deals with lower bounds for the remainder term in asymptotics for a certain class of arithmetic functions. Typically, these are generated by a Dirichlet series of the form ζ 2(s)ζ(2s−1)ζ M(2s)H(s), where M is an arbitrary integer and H(s) has an Euler product which converges absolutely for R s > σ0, with some fixed σ0 < 1/2.
Bounds for double zeta-functions
Isao Kiuchi, Yoshio Tanigawa (2006)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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In this paper we shall derive the order of magnitude for the double zeta-functionof Euler-Zagier type in the region .First we prepare the Euler-Maclaurinsummation formula in a suitable form for our purpose, and then we apply the theory of doubleexponential sums of van der Corput’s type.
On the order of the Mertens function.
Kotnik, Tadej, van de Lune, Jan (2004)
Experimental Mathematics
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An explicit formula of Atkinson type for the product of the Riemann zeta-function and a Dirichlet polynomial
Hideaki Ishikawa, Kohji Matsumoto (2011)
Open Mathematics
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We prove an explicit formula of Atkinson type for the error term in the asymptotic formula for the mean square of the product of the Riemann zeta-function and a Dirichlet polynomial. To deal with the case when coefficients of the Dirichlet polynomial are complex, we apply the idea of the first author in his study on mean values of Dirichlet L-functions.
Estimates of convolutions of certain number-theoretic error terms.
Ivić, Aleksandar (2004)
International Journal of Mathematics and Mathematical Sciences
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On zeta-functions associated to certain cusp forms. II
Antanas Laurinčikas, Joern Steuding, Darius Šiaučiūnas (2009)
Open Mathematics
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A formula for the mean value of multiplicative functions associated to certain cusp forms is obtained. The paper is a continuation of [4].