scholarly journals The average behaviour of the error term in a new kind of the divisor problem

2016 ◽  
Vol 438 (2) ◽  
pp. 533-550 ◽  
Author(s):  
Debika Banerjee ◽  
Makoto Minamide
Keyword(s):  
Error Term ◽  
Divisor Problem ◽  
Average Behaviour

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]).

Two classical lattice point problems

1961 ◽  
Vol 57 (4) ◽  
pp. 699-721 ◽  
Author(s):  
K. S. Gangadharan ◽  
A. E. Ingham
Keyword(s):  
Lattice Point ◽  
Error Term ◽  
Divisor Problem ◽  
Lattice Points ◽  
Classical Lattice ◽  
Rectangular Hyperbola ◽  
Number Of Divisors ◽  
Image Position ◽  
Euler's Constant ◽  
Lattice Point Problems

Let r(n) be the number of representations of n as a sum of two squares, d(n) the number of divisors of n, andwhere γ is Euler's constant. Then P(x) is the error term in the problem of the lattice points of the circle, and Δ(x) the error term in Dirichlet's divisor problem, or the problem of the lattice points of the rectangular hyperbola.

scholarly journals Mean square of the error term in the asymmetric multidimensional divisor problem

2016 ◽  
Vol 54 (2) ◽  
pp. 173-193 ◽  
Author(s):  
Xiaodon Cao ◽  
Yoshio Tanigawa ◽  
Wenguang Zhai
Keyword(s):  
Error Term ◽  
Divisor Problem ◽  
Mean Square

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.

scholarly journals On the higher moments of the error term in the divisor problem

2007 ◽  
Vol 51 (2) ◽  
pp. 353-377 ◽  
Author(s):  
Aleksandar Ivić ◽  
Patrick Sargos
Keyword(s):  
Error Term ◽  
Divisor Problem ◽  
Higher Moments

Large values of the error term in the divisor problem

1983 ◽  
Vol 71 (3) ◽  
pp. 513-520 ◽  
Author(s):  
Aleksandar Ivić
Keyword(s):  
Error Term ◽  
Divisor Problem

scholarly journals On a generalized divisor problem I

2002 ◽  
Vol 165 ◽  
pp. 71-78 ◽  
Author(s):  
Yuk-Kam Lau
Keyword(s):  
Error Term ◽  
Divisor Problem ◽  
Sign Changes ◽  
Oscillatory Nature ◽  
Dirichlet Divisor Problem

We give a discussion on the properties of Δa(x) (− 1 < a < 0), which is a generalization of the error term Δ(x) in the Dirichlet divisor problem. In particular, we study its oscillatory nature and investigate the gaps between its sign-changes for −½ ≤ a < 0.

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