The average behaviour of the error term in a new kind of the divisor problem
Debika Banerjee,Makoto Minamide +1 more
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TLDR
In this paper, a new kind of divisor function D ( 1 ) ( n ) by the nth coefficient of the Dirichlet series was defined and the error term in the asymptotic formula for ∑ n ≤ x D( 1 )( n ).About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 2016-06-15 and is currently open access. It has received 6 citations till now. The article focuses on the topics: Divisor summatory function & Divisor function.read more
Citations
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On higher-power moments of $$\Delta_{(1)}(x)$$Δ(1)(x)
TL;DR: In this paper, the higher power moments of the Dirichlet series were studied and asymptotic formulas were derived for the error term of the sum of the error terms.
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On the higher moments of the error term in the divisor problem
Aleksandar Ivić,Patrick Sargos +1 more
TL;DR: In this paper, asymptotic formulas for the error term in the Dirichlet divisor problem were derived for the integrals of the errors of the error terms of Δ(x) and δ(x), respectively.
Journal ArticleDOI
Titchmarsh’s Method for the Approximate Functional Equations for
TL;DR: In this article, the authors remove this factor from these three error terms by using the method of Titchmarsh, and then they use this factor to remove the error term.
Journal ArticleDOI
Sign changes of Δ(1)(x)
TL;DR: For a sufficiently large constant c1 and a large T, it was shown in this article that for a small constant c2 there exist infinitely many subintervals in [T,2T] such that ±Δ(1)(x)>c2t1/4log2t holds on these subinterval.
References
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Book
The Theory of the Riemann Zeta-Function
TL;DR: The Riemann zeta-function embodies both additive and multiplicative structures in a single function, making it one of the most important tools in the study of prime numbers as mentioned in this paper.
Book
The Riemann Zeta-Function
TL;DR: For Re s = σ > 1, the Riemann zeta function ζ(s) is defined by as discussed by the authors, and it follows from the definition that ζ is an analytic function in the halfplane Re s > 1.
Journal ArticleDOI
Exponential sums and lattice points III
TL;DR: In the case of the Dirichlet divisor problem, the number of points of the integer lattice in a planar domain bounded by a piecewise smooth curve has been shown to be upper bounded by the radius of the maximum radius of curvature as mentioned in this paper.
Related Papers (5)
On the higher moments of the error term in the divisor problem
Aleksandar Ivić,Patrick Sargos +1 more