Means of powers of the zeta function
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It is well known that the Lindel"of Hypothesis is equivalent to the statement that $$frac 1Tint_0^T|zeta(1/2=it)|^{2k} =O(T^epsilon)$$ for all positive integers $k$ and all positive real $epsilon$, and these fact are known for $k=1, 2$. May I ask you for references to the proofs.
reference-request analytic-number-theory riemann-zeta
asked Dec 6 '18 at 19:59
DuracDurac
113
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add a comment |
0
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It is well known that the Lindel"of Hypothesis is equivalent to the statement that $$frac 1Tint_0^T|zeta(1/2=it)|^{2k} =O(T^epsilon)$$ for all positive integers $k$ and all positive real $epsilon$, and these fact are known for $k=1, 2$. May I ask you for references to the proofs.
reference-request analytic-number-theory riemann-zeta
asked Dec 6 '18 at 19:59
DuracDurac
113
$endgroup$
$begingroup$
In papers and chapters (Titchmarsh and others) about the Dirichlet divisor problem
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– reuns
Dec 6 '18 at 20:16
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Do you mean the equivalence? I am interested in the proofs of the estimate for $k=1, 2$.
$endgroup$
– Durac
Dec 6 '18 at 20:27
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zulfahmed.files.wordpress.com/2018/08/… p.74-75
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– reuns
Dec 6 '18 at 20:40
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Thanks! Just a remark: this is the chapter of Titchmarsh titled 'Mean value theorems'. (You have answered my question, I am ready to accept.)
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– Durac
Dec 6 '18 at 20:51
add a comment |
0
0
0
$begingroup$
It is well known that the Lindel"of Hypothesis is equivalent to the statement that $$frac 1Tint_0^T|zeta(1/2=it)|^{2k} =O(T^epsilon)$$ for all positive integers $k$ and all positive real $epsilon$, and these fact are known for $k=1, 2$. May I ask you for references to the proofs.
reference-request analytic-number-theory riemann-zeta
asked Dec 6 '18 at 19:59
DuracDurac
113
$endgroup$
It is well known that the Lindel"of Hypothesis is equivalent to the statement that $$frac 1Tint_0^T|zeta(1/2=it)|^{2k} =O(T^epsilon)$$ for all positive integers $k$ and all positive real $epsilon$, and these fact are known for $k=1, 2$. May I ask you for references to the proofs.
reference-request analytic-number-theory riemann-zeta
reference-request analytic-number-theory riemann-zeta
asked Dec 6 '18 at 19:59
DuracDurac
113
asked Dec 6 '18 at 19:59
DuracDurac
113
asked Dec 6 '18 at 19:59
DuracDurac
113
asked Dec 6 '18 at 19:59
DuracDurac
113
asked Dec 6 '18 at 19:59
DuracDurac
113
113
$begingroup$
In papers and chapters (Titchmarsh and others) about the Dirichlet divisor problem
$endgroup$
– reuns
Dec 6 '18 at 20:16
$begingroup$
Do you mean the equivalence? I am interested in the proofs of the estimate for $k=1, 2$.
$endgroup$
– Durac
Dec 6 '18 at 20:27
$begingroup$
zulfahmed.files.wordpress.com/2018/08/… p.74-75
$endgroup$
– reuns
Dec 6 '18 at 20:40
$begingroup$
Thanks! Just a remark: this is the chapter of Titchmarsh titled 'Mean value theorems'. (You have answered my question, I am ready to accept.)
$endgroup$
– Durac
Dec 6 '18 at 20:51
add a comment |
$begingroup$
In papers and chapters (Titchmarsh and others) about the Dirichlet divisor problem
$endgroup$
– reuns
Dec 6 '18 at 20:16
$begingroup$
Do you mean the equivalence? I am interested in the proofs of the estimate for $k=1, 2$.
$endgroup$
– Durac
Dec 6 '18 at 20:27
$begingroup$
zulfahmed.files.wordpress.com/2018/08/… p.74-75
$endgroup$
– reuns
Dec 6 '18 at 20:40
$begingroup$
Thanks! Just a remark: this is the chapter of Titchmarsh titled 'Mean value theorems'. (You have answered my question, I am ready to accept.)
$endgroup$
– Durac
Dec 6 '18 at 20:51
$begingroup$
In papers and chapters (Titchmarsh and others) about the Dirichlet divisor problem
$endgroup$
– reuns
Dec 6 '18 at 20:16
$begingroup$
In papers and chapters (Titchmarsh and others) about the Dirichlet divisor problem
$endgroup$
– reuns
Dec 6 '18 at 20:16
$begingroup$
Do you mean the equivalence? I am interested in the proofs of the estimate for $k=1, 2$.
$endgroup$
– Durac
Dec 6 '18 at 20:27
$begingroup$
Do you mean the equivalence? I am interested in the proofs of the estimate for $k=1, 2$.
$endgroup$
– Durac
Dec 6 '18 at 20:27
$begingroup$
zulfahmed.files.wordpress.com/2018/08/… p.74-75
$endgroup$
– reuns
Dec 6 '18 at 20:40
$begingroup$
zulfahmed.files.wordpress.com/2018/08/… p.74-75
$endgroup$
– reuns
Dec 6 '18 at 20:40
$begingroup$
Thanks! Just a remark: this is the chapter of Titchmarsh titled 'Mean value theorems'. (You have answered my question, I am ready to accept.)
$endgroup$
– Durac
Dec 6 '18 at 20:51
$begingroup$
Thanks! Just a remark: this is the chapter of Titchmarsh titled 'Mean value theorems'. (You have answered my question, I am ready to accept.)
$endgroup$
– Durac
Dec 6 '18 at 20:51
add a comment |
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$begingroup$
In papers and chapters (Titchmarsh and others) about the Dirichlet divisor problem
$endgroup$
– reuns
Dec 6 '18 at 20:16
$begingroup$
Do you mean the equivalence? I am interested in the proofs of the estimate for $k=1, 2$.
$endgroup$
– Durac
Dec 6 '18 at 20:27
$begingroup$
zulfahmed.files.wordpress.com/2018/08/… p.74-75
$endgroup$
– reuns
Dec 6 '18 at 20:40
$begingroup$
Thanks! Just a remark: this is the chapter of Titchmarsh titled 'Mean value theorems'. (You have answered my question, I am ready to accept.)
$endgroup$
– Durac
Dec 6 '18 at 20:51