The growth-rate of a sum over a prime-counting function thing
$begingroup$
What might the growth rate of
$$S(n)=sum_{k=1}^{lfloor n/2 rfloor-1} pi(n-2k)^{k+1}$$
(where $pi$ is being used to represent the prime-counting function) be and what techniques are suggested to prove it?
Is the prime number theorem needed here?
(I am trying to use this function as a way to bound another one)
number-theory prime-numbers asymptotics
asked Jan 6 at 16:44
Cardioid_Ass_22Cardioid_Ass_22
44315
$endgroup$
add a comment |
$begingroup$
What might the growth rate of
$$S(n)=sum_{k=1}^{lfloor n/2 rfloor-1} pi(n-2k)^{k+1}$$
(where $pi$ is being used to represent the prime-counting function) be and what techniques are suggested to prove it?
Is the prime number theorem needed here?
(I am trying to use this function as a way to bound another one)
number-theory prime-numbers asymptotics
asked Jan 6 at 16:44
Cardioid_Ass_22Cardioid_Ass_22
44315
$endgroup$
add a comment |
$begingroup$
What might the growth rate of
$$S(n)=sum_{k=1}^{lfloor n/2 rfloor-1} pi(n-2k)^{k+1}$$
(where $pi$ is being used to represent the prime-counting function) be and what techniques are suggested to prove it?
Is the prime number theorem needed here?
(I am trying to use this function as a way to bound another one)
number-theory prime-numbers asymptotics
asked Jan 6 at 16:44
Cardioid_Ass_22Cardioid_Ass_22
44315
$endgroup$
What might the growth rate of
$$S(n)=sum_{k=1}^{lfloor n/2 rfloor-1} pi(n-2k)^{k+1}$$
(where $pi$ is being used to represent the prime-counting function) be and what techniques are suggested to prove it?
Is the prime number theorem needed here?
(I am trying to use this function as a way to bound another one)
number-theory prime-numbers asymptotics
number-theory prime-numbers asymptotics
asked Jan 6 at 16:44
Cardioid_Ass_22Cardioid_Ass_22
44315
asked Jan 6 at 16:44
Cardioid_Ass_22Cardioid_Ass_22
44315
asked Jan 6 at 16:44
Cardioid_Ass_22Cardioid_Ass_22
44315
asked Jan 6 at 16:44
Cardioid_Ass_22Cardioid_Ass_22
44315
asked Jan 6 at 16:44
Cardioid_Ass_22Cardioid_Ass_22
44315
44315
add a comment |
add a comment |
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