Dirichlet series with a single zeroContinuation up to zero of a Dirichlet series with bounded coefficientsSome Dirichlet series questions.Convergence of Dirichlet seriesAbscissa of convergence of Dirichlet seriesThe abscissa of convergence of the real part of a Dirichlet seriesGap Between Abscissae of Conditional Convergence and Holomorphicity for Dirichlet SeriesTwin prime based Dirichlet seriesQuestion on a generalized Dirichlet seriesWhich complex maps with branch cuts have a representation by Dirichlet series?meromorphic extension of dirichlet series
Dirichlet series with a single zero
Continuation up to zero of a Dirichlet series with bounded coefficientsSome Dirichlet series questions.Convergence of Dirichlet seriesAbscissa of convergence of Dirichlet seriesThe abscissa of convergence of the real part of a Dirichlet seriesGap Between Abscissae of Conditional Convergence and Holomorphicity for Dirichlet SeriesTwin prime based Dirichlet seriesQuestion on a generalized Dirichlet seriesWhich complex maps with branch cuts have a representation by Dirichlet series?meromorphic extension of dirichlet series
$begingroup$
I need to find a Dirichlet series f that has the following property.
f is zero in only one point s such that Re(s) > $sigma_c $.
nt.number-theory cv.complex-variables analytic-number-theory dirichlet-series
edited May 4 at 17:42
Lucia
35.5k5153180
asked May 4 at 14:19
CluelessClueless
772
New contributor
Clueless is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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$endgroup$
|
show 1 more comment
$begingroup$
I need to find a Dirichlet series f that has the following property.
f is zero in only one point s such that Re(s) > $sigma_c $.
nt.number-theory cv.complex-variables analytic-number-theory dirichlet-series
edited May 4 at 17:42
Lucia
35.5k5153180
asked May 4 at 14:19
CluelessClueless
772
New contributor
Clueless is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
$1/zeta(s)$
$endgroup$
– Wojowu
May 4 at 16:04
7
$begingroup$
Why are people voting to close this?
$endgroup$
– Lucia
May 4 at 16:54
4
$begingroup$
@Lucia I have voted to close because I thought $1/zeta(s)$ is a (relatively) obvious counterexample, but I have not realized it relies on RH. I have retracted my vote now.
$endgroup$
– Wojowu
May 4 at 17:51
3
$begingroup$
Just curious: why did you need to find such an example?
$endgroup$
– KConrad
2 days ago
1
$begingroup$
@Jan-ChristophSchlage-Puchta $sigma_c$ is a standard notation for the abscissa of convergence, while abscissa of absolute convergence is usually denoted with $sigma_a$.
$endgroup$
– Wojowu
yesterday
|
show 1 more comment
$begingroup$
I need to find a Dirichlet series f that has the following property.
f is zero in only one point s such that Re(s) > $sigma_c $.
nt.number-theory cv.complex-variables analytic-number-theory dirichlet-series
edited May 4 at 17:42
Lucia
35.5k5153180
asked May 4 at 14:19
CluelessClueless
772
New contributor
Clueless is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I need to find a Dirichlet series f that has the following property.
f is zero in only one point s such that Re(s) > $sigma_c $.
nt.number-theory cv.complex-variables analytic-number-theory dirichlet-series
nt.number-theory cv.complex-variables analytic-number-theory dirichlet-series
edited May 4 at 17:42
Lucia
35.5k5153180
asked May 4 at 14:19
CluelessClueless
772
New contributor
Clueless is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited May 4 at 17:42
Lucia
35.5k5153180
asked May 4 at 14:19
CluelessClueless
772
New contributor
Clueless is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited May 4 at 17:42
Lucia
35.5k5153180
edited May 4 at 17:42
Lucia
35.5k5153180
edited May 4 at 17:42
Lucia
35.5k5153180
35.5k5153180
asked May 4 at 14:19
CluelessClueless
772
New contributor
Clueless is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked May 4 at 14:19
CluelessClueless
772
asked May 4 at 14:19
CluelessClueless
772
772
New contributor
Clueless is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Clueless is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
$begingroup$
$1/zeta(s)$
$endgroup$
– Wojowu
May 4 at 16:04
7
$begingroup$
Why are people voting to close this?
$endgroup$
– Lucia
May 4 at 16:54
4
$begingroup$
@Lucia I have voted to close because I thought $1/zeta(s)$ is a (relatively) obvious counterexample, but I have not realized it relies on RH. I have retracted my vote now.
$endgroup$
– Wojowu
May 4 at 17:51
3
$begingroup$
Just curious: why did you need to find such an example?
$endgroup$
– KConrad
2 days ago
1
$begingroup$
@Jan-ChristophSchlage-Puchta $sigma_c$ is a standard notation for the abscissa of convergence, while abscissa of absolute convergence is usually denoted with $sigma_a$.
$endgroup$
– Wojowu
yesterday
|
show 1 more comment
1
$begingroup$
$1/zeta(s)$
$endgroup$
– Wojowu
May 4 at 16:04
7
$begingroup$
Why are people voting to close this?
$endgroup$
– Lucia
May 4 at 16:54
4
$begingroup$
@Lucia I have voted to close because I thought $1/zeta(s)$ is a (relatively) obvious counterexample, but I have not realized it relies on RH. I have retracted my vote now.
$endgroup$
– Wojowu
May 4 at 17:51
3
$begingroup$
Just curious: why did you need to find such an example?
$endgroup$
– KConrad
2 days ago
1
$begingroup$
@Jan-ChristophSchlage-Puchta $sigma_c$ is a standard notation for the abscissa of convergence, while abscissa of absolute convergence is usually denoted with $sigma_a$.
$endgroup$
– Wojowu
yesterday
1
1
$begingroup$
$1/zeta(s)$
$endgroup$
– Wojowu
May 4 at 16:04
$begingroup$
$1/zeta(s)$
$endgroup$
– Wojowu
May 4 at 16:04
7
7
$begingroup$
Why are people voting to close this?
$endgroup$
– Lucia
May 4 at 16:54
$begingroup$
Why are people voting to close this?
$endgroup$
– Lucia
May 4 at 16:54
4
4
$begingroup$
@Lucia I have voted to close because I thought $1/zeta(s)$ is a (relatively) obvious counterexample, but I have not realized it relies on RH. I have retracted my vote now.
$endgroup$
– Wojowu
May 4 at 17:51
$begingroup$
@Lucia I have voted to close because I thought $1/zeta(s)$ is a (relatively) obvious counterexample, but I have not realized it relies on RH. I have retracted my vote now.
$endgroup$
– Wojowu
May 4 at 17:51
3
3
$begingroup$
Just curious: why did you need to find such an example?
$endgroup$
– KConrad
2 days ago
$begingroup$
Just curious: why did you need to find such an example?
$endgroup$
– KConrad
2 days ago
1
1
$begingroup$
@Jan-ChristophSchlage-Puchta $sigma_c$ is a standard notation for the abscissa of convergence, while abscissa of absolute convergence is usually denoted with $sigma_a$.
$endgroup$
– Wojowu
yesterday
$begingroup$
@Jan-ChristophSchlage-Puchta $sigma_c$ is a standard notation for the abscissa of convergence, while abscissa of absolute convergence is usually denoted with $sigma_a$.
$endgroup$
– Wojowu
yesterday
|
show 1 more comment
1 Answer
1
active
oldest
votes
$begingroup$
That such a Dirichlet series exists was a conjecture of Balazard, which was
recently resolved by Hilberdink and Saias. If the Riemann Hypothesis is
true, then $1/zeta(s)$ would provide such an example (with the abscissa of conditional convergence being $1/2$), and the goal was to find an unconditional example.
answered May 4 at 16:54
LuciaLucia
35.5k5153180
$endgroup$
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1 Answer
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$begingroup$
That such a Dirichlet series exists was a conjecture of Balazard, which was
recently resolved by Hilberdink and Saias. If the Riemann Hypothesis is
true, then $1/zeta(s)$ would provide such an example (with the abscissa of conditional convergence being $1/2$), and the goal was to find an unconditional example.
answered May 4 at 16:54
LuciaLucia
35.5k5153180
$endgroup$
add a comment |
$begingroup$
That such a Dirichlet series exists was a conjecture of Balazard, which was
recently resolved by Hilberdink and Saias. If the Riemann Hypothesis is
true, then $1/zeta(s)$ would provide such an example (with the abscissa of conditional convergence being $1/2$), and the goal was to find an unconditional example.
answered May 4 at 16:54
LuciaLucia
35.5k5153180
$endgroup$
add a comment |
$begingroup$
That such a Dirichlet series exists was a conjecture of Balazard, which was
recently resolved by Hilberdink and Saias. If the Riemann Hypothesis is
true, then $1/zeta(s)$ would provide such an example (with the abscissa of conditional convergence being $1/2$), and the goal was to find an unconditional example.
answered May 4 at 16:54
LuciaLucia
35.5k5153180
$endgroup$
That such a Dirichlet series exists was a conjecture of Balazard, which was
recently resolved by Hilberdink and Saias. If the Riemann Hypothesis is
true, then $1/zeta(s)$ would provide such an example (with the abscissa of conditional convergence being $1/2$), and the goal was to find an unconditional example.
answered May 4 at 16:54
LuciaLucia
35.5k5153180
answered May 4 at 16:54
LuciaLucia
35.5k5153180
answered May 4 at 16:54
LuciaLucia
35.5k5153180
answered May 4 at 16:54
LuciaLucia
35.5k5153180
35.5k5153180
add a comment |
add a comment |
Clueless is a new contributor. Be nice, and check out our Code of Conduct.
Clueless is a new contributor. Be nice, and check out our Code of Conduct.
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1
$begingroup$
$1/zeta(s)$
$endgroup$
– Wojowu
May 4 at 16:04
7
$begingroup$
Why are people voting to close this?
$endgroup$
– Lucia
May 4 at 16:54
4
$begingroup$
@Lucia I have voted to close because I thought $1/zeta(s)$ is a (relatively) obvious counterexample, but I have not realized it relies on RH. I have retracted my vote now.
$endgroup$
– Wojowu
May 4 at 17:51
3
$begingroup$
Just curious: why did you need to find such an example?
$endgroup$
– KConrad
2 days ago
1
$begingroup$
@Jan-ChristophSchlage-Puchta $sigma_c$ is a standard notation for the abscissa of convergence, while abscissa of absolute convergence is usually denoted with $sigma_a$.
$endgroup$
– Wojowu
yesterday