New estimates of the remainder in an asymptotic formula in the multidimensional Dirichlet divisor problem

2011 ◽  
Vol 89 (3-4) ◽  
pp. 504-518
Author(s):  
O. V. Kolpakova
Keyword(s):  
Asymptotic Formula ◽  
Divisor Problem ◽  
Dirichlet Divisor Problem

The Dirichlet Divisor Problem of Arithmetic Progressions

2016 ◽  
Vol 59 (3) ◽  
pp. 592-598
Author(s):  
H. Q. Liu
Keyword(s):  
Asymptotic Formula ◽  
Divisor Problem ◽  
Arithmetic Progressions ◽  
Elementary Method ◽  
Dirichlet Divisor Problem ◽  
Better Than

AbstractWe present an elementary method for studying the problem of getting an asymptotic formula that is better than Hooley’s and Heath-Brown’s results for certain cases.

scholarly journals Estimates of convolutions of certain number-theoretic error terms

2004 ◽  
Vol 2004 (1) ◽  
pp. 1-23 ◽  
Author(s):  
Aleksandar Ivic
Keyword(s):  
Asymptotic Formula ◽  
Error Term ◽  
Abelian Groups ◽  
Divisor Problem ◽  
Dirichlet Divisor Problem ◽  
Error Terms ◽  
Convolution Function

Several estimates for the convolution functionC [f(x)]:=∫1xf(y) f(x/y)(dy/y)and its iterates are obtained whenf(x)is a suitable number-theoretic error term. We deal with the case of the asymptotic formula for∫0T|ζ(1/2+it)|2kdt(k=1,2), the general Dirichlet divisor problem, the problem of nonisomorphic Abelian groups of given order, and the Rankin-Selberg convolution.

On the seventh power moment of Δ(x)

2017 ◽  
Vol 13 (03) ◽  
pp. 571-591
Author(s):  
Jinjiang Li
Keyword(s):  
Asymptotic Formula ◽  
Error Term ◽  
Divisor Problem ◽  
Power Moment ◽  
Dirichlet Divisor Problem

Let [Formula: see text] be the error term of the Dirichlet divisor problem. In this paper, we establish an asymptotic formula of the seventh-power moment of [Formula: see text] and prove that [Formula: see text] with [Formula: see text] which improves the previous result.

scholarly journals Remark on Smith’s result on a divisor problem in arithmetic progressions

1985 ◽  
Vol 98 ◽  
pp. 37-42 ◽  
Author(s):  
Kohji Matsumoto
Keyword(s):  
Asymptotic Formula ◽  
Error Term ◽  
Divisor Problem ◽  
Arithmetic Progressions ◽  
Euler Function

Let dk(n) be the number of the factorizations of n into k positive numbers. It is known that the following asymptotic formula holds: where r and q are co-prime integers with 0 < r < q, Pk is a polynomial of degree k − 1, φ(q) is the Euler function, and Δk(q; r) is the error term. (See Lavrik [3]).

scholarly journals On the Dirichlet divisor problem in short intervals

2013 ◽  
Vol 33 (3) ◽  
pp. 447-465 ◽  
Author(s):  
Aleksandar Ivić ◽  
Wenguang Zhai
Keyword(s):  
Divisor Problem ◽  
Short Intervals ◽  
Dirichlet Divisor Problem

scholarly journals On the mean square of the Riemann zeta function and the divisor problem

2008 ◽  
Vol 83 (97) ◽  
pp. 71-86
Author(s):  
Yifan Yang
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Integral Transforms ◽  
Divisor Problem ◽  
Mean Square ◽  
The Riemann Zeta Function ◽  
Dirichlet Divisor Problem ◽  
Error Terms ◽  
Riemann Zeta ◽  
The Mean

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.

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