Truncated sum of divisors bound
$begingroup$
I am interested in an upper bound for
$$
sum_{substack{d|N\ d>A}}frac{1}{d^3},$$
in particular, I can get the above to be
$$sum_{substack{d|N\ d>A}}frac{1}{d^3}ll frac{text{exp}left(C frac{log(N)}{loglog(N)}right)}{A^3}$$
for some positive constant $C$. However I would like to do better. I think that the upper bound should be around
$$ frac{log^C(N)}{A^3}$$
for some other positive constant $C.$
We also have that $A<N^{1/2}.$
References are welcome.
number-theory analytic-number-theory divisor-sum divisor-counting-function
asked Jan 10 at 23:41
user164144user164144
515
$endgroup$
add a comment |
$begingroup$
I am interested in an upper bound for
$$
sum_{substack{d|N\ d>A}}frac{1}{d^3},$$
in particular, I can get the above to be
$$sum_{substack{d|N\ d>A}}frac{1}{d^3}ll frac{text{exp}left(C frac{log(N)}{loglog(N)}right)}{A^3}$$
for some positive constant $C$. However I would like to do better. I think that the upper bound should be around
$$ frac{log^C(N)}{A^3}$$
for some other positive constant $C.$
We also have that $A<N^{1/2}.$
References are welcome.
number-theory analytic-number-theory divisor-sum divisor-counting-function
asked Jan 10 at 23:41
user164144user164144
515
$endgroup$
add a comment |
$begingroup$
I am interested in an upper bound for
$$
sum_{substack{d|N\ d>A}}frac{1}{d^3},$$
in particular, I can get the above to be
$$sum_{substack{d|N\ d>A}}frac{1}{d^3}ll frac{text{exp}left(C frac{log(N)}{loglog(N)}right)}{A^3}$$
for some positive constant $C$. However I would like to do better. I think that the upper bound should be around
$$ frac{log^C(N)}{A^3}$$
for some other positive constant $C.$
We also have that $A<N^{1/2}.$
References are welcome.
number-theory analytic-number-theory divisor-sum divisor-counting-function
asked Jan 10 at 23:41
user164144user164144
515
$endgroup$
I am interested in an upper bound for
$$
sum_{substack{d|N\ d>A}}frac{1}{d^3},$$
in particular, I can get the above to be
$$sum_{substack{d|N\ d>A}}frac{1}{d^3}ll frac{text{exp}left(C frac{log(N)}{loglog(N)}right)}{A^3}$$
for some positive constant $C$. However I would like to do better. I think that the upper bound should be around
$$ frac{log^C(N)}{A^3}$$
for some other positive constant $C.$
We also have that $A<N^{1/2}.$
References are welcome.
number-theory analytic-number-theory divisor-sum divisor-counting-function
number-theory analytic-number-theory divisor-sum divisor-counting-function
asked Jan 10 at 23:41
user164144user164144
515
asked Jan 10 at 23:41
user164144user164144
515
edited Jan 10 at 23:53
user164144
asked Jan 10 at 23:41
user164144user164144
515
asked Jan 10 at 23:41
user164144user164144
515
asked Jan 10 at 23:41
user164144user164144
515
515
add a comment |
add a comment |
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