Line of Symmetry of the Zeta Function
0
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I heard once that 0.5 is the line of symmetry of the Riemann Zeta Function. What does that mean? A graph illustrating would be helpful.
riemann-zeta symmetry
asked Jan 16 at 12:36
JamesJames
218
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show 10 more comments
0
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I heard once that 0.5 is the line of symmetry of the Riemann Zeta Function. What does that mean? A graph illustrating would be helpful.
riemann-zeta symmetry
asked Jan 16 at 12:36
JamesJames
218
$endgroup$
$begingroup$
It means that values with $Re(s)<1/2$ are fixed by the values with $Re(s)>1/2$ due to the functional equation.
$endgroup$
– Diger
Jan 16 at 12:40
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So for example zeta(0.6+14i) is equal to zeta(0.4+14i)?
$endgroup$
– James
Jan 16 at 12:41
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en.wikipedia.org/wiki/Riemann_Xi_function \ en.wikipedia.org/wiki/Riemann_zeta_function
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– Diger
Jan 16 at 12:42
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I don't read German.
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– James
Jan 16 at 12:43
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The symmetry comes more into light using the $Xi$ function which is an even function.
$endgroup$
– Diger
Jan 16 at 12:45
|
show 10 more comments
0
0
0
$begingroup$
I heard once that 0.5 is the line of symmetry of the Riemann Zeta Function. What does that mean? A graph illustrating would be helpful.
riemann-zeta symmetry
asked Jan 16 at 12:36
JamesJames
218
$endgroup$
I heard once that 0.5 is the line of symmetry of the Riemann Zeta Function. What does that mean? A graph illustrating would be helpful.
riemann-zeta symmetry
riemann-zeta symmetry
asked Jan 16 at 12:36
JamesJames
218
asked Jan 16 at 12:36
JamesJames
218
asked Jan 16 at 12:36
JamesJames
218
asked Jan 16 at 12:36
JamesJames
218
asked Jan 16 at 12:36
JamesJames
218
218
$begingroup$
It means that values with $Re(s)<1/2$ are fixed by the values with $Re(s)>1/2$ due to the functional equation.
$endgroup$
– Diger
Jan 16 at 12:40
$begingroup$
So for example zeta(0.6+14i) is equal to zeta(0.4+14i)?
$endgroup$
– James
Jan 16 at 12:41
$begingroup$
en.wikipedia.org/wiki/Riemann_Xi_function \ en.wikipedia.org/wiki/Riemann_zeta_function
$endgroup$
– Diger
Jan 16 at 12:42
$begingroup$
I don't read German.
$endgroup$
– James
Jan 16 at 12:43
$begingroup$
The symmetry comes more into light using the $Xi$ function which is an even function.
$endgroup$
– Diger
Jan 16 at 12:45
|
show 10 more comments
$begingroup$
It means that values with $Re(s)<1/2$ are fixed by the values with $Re(s)>1/2$ due to the functional equation.
$endgroup$
– Diger
Jan 16 at 12:40
$begingroup$
So for example zeta(0.6+14i) is equal to zeta(0.4+14i)?
$endgroup$
– James
Jan 16 at 12:41
$begingroup$
en.wikipedia.org/wiki/Riemann_Xi_function \ en.wikipedia.org/wiki/Riemann_zeta_function
$endgroup$
– Diger
Jan 16 at 12:42
$begingroup$
I don't read German.
$endgroup$
– James
Jan 16 at 12:43
$begingroup$
The symmetry comes more into light using the $Xi$ function which is an even function.
$endgroup$
– Diger
Jan 16 at 12:45
$begingroup$
It means that values with $Re(s)<1/2$ are fixed by the values with $Re(s)>1/2$ due to the functional equation.
$endgroup$
– Diger
Jan 16 at 12:40
$begingroup$
It means that values with $Re(s)<1/2$ are fixed by the values with $Re(s)>1/2$ due to the functional equation.
$endgroup$
– Diger
Jan 16 at 12:40
$begingroup$
So for example zeta(0.6+14i) is equal to zeta(0.4+14i)?
$endgroup$
– James
Jan 16 at 12:41
$begingroup$
So for example zeta(0.6+14i) is equal to zeta(0.4+14i)?
$endgroup$
– James
Jan 16 at 12:41
$begingroup$
en.wikipedia.org/wiki/Riemann_Xi_function \ en.wikipedia.org/wiki/Riemann_zeta_function
$endgroup$
– Diger
Jan 16 at 12:42
$begingroup$
en.wikipedia.org/wiki/Riemann_Xi_function \ en.wikipedia.org/wiki/Riemann_zeta_function
$endgroup$
– Diger
Jan 16 at 12:42
$begingroup$
I don't read German.
$endgroup$
– James
Jan 16 at 12:43
$begingroup$
I don't read German.
$endgroup$
– James
Jan 16 at 12:43
$begingroup$
The symmetry comes more into light using the $Xi$ function which is an even function.
$endgroup$
– Diger
Jan 16 at 12:45
$begingroup$
The symmetry comes more into light using the $Xi$ function which is an even function.
$endgroup$
– Diger
Jan 16 at 12:45
|
show 10 more comments
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$begingroup$
It means that values with $Re(s)<1/2$ are fixed by the values with $Re(s)>1/2$ due to the functional equation.
$endgroup$
– Diger
Jan 16 at 12:40
$begingroup$
So for example zeta(0.6+14i) is equal to zeta(0.4+14i)?
$endgroup$
– James
Jan 16 at 12:41
$begingroup$
en.wikipedia.org/wiki/Riemann_Xi_function \ en.wikipedia.org/wiki/Riemann_zeta_function
$endgroup$
– Diger
Jan 16 at 12:42
$begingroup$
I don't read German.
$endgroup$
– James
Jan 16 at 12:43
$begingroup$
The symmetry comes more into light using the $Xi$ function which is an even function.
$endgroup$
– Diger
Jan 16 at 12:45