On the behavior of $|zeta(1/2 + it)|$ for $tin(-14,14)$
Denote by $zeta$ the Riemann zeta function.
Since $zeta(1/2 + it)neq 0$ for $|t|leq 14$, it seems to follow that $|zeta(1/2 + it)|$ is either strictly decreasing or strictly increasing on $(-14,14)$. But what exactly is the behaviour of $|zeta(1/2 +it)|$ on this region ? I mean, is it strictly increasing or is it strictly decreasing ?
A graphical sketch might help.
number-theory analytic-number-theory riemann-zeta
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Denote by $zeta$ the Riemann zeta function.
Since $zeta(1/2 + it)neq 0$ for $|t|leq 14$, it seems to follow that $|zeta(1/2 + it)|$ is either strictly decreasing or strictly increasing on $(-14,14)$. But what exactly is the behaviour of $|zeta(1/2 +it)|$ on this region ? I mean, is it strictly increasing or is it strictly decreasing ?
A graphical sketch might help.
number-theory analytic-number-theory riemann-zeta
add a comment |
Denote by $zeta$ the Riemann zeta function.
Since $zeta(1/2 + it)neq 0$ for $|t|leq 14$, it seems to follow that $|zeta(1/2 + it)|$ is either strictly decreasing or strictly increasing on $(-14,14)$. But what exactly is the behaviour of $|zeta(1/2 +it)|$ on this region ? I mean, is it strictly increasing or is it strictly decreasing ?
A graphical sketch might help.
number-theory analytic-number-theory riemann-zeta
Denote by $zeta$ the Riemann zeta function.
Since $zeta(1/2 + it)neq 0$ for $|t|leq 14$, it seems to follow that $|zeta(1/2 + it)|$ is either strictly decreasing or strictly increasing on $(-14,14)$. But what exactly is the behaviour of $|zeta(1/2 +it)|$ on this region ? I mean, is it strictly increasing or is it strictly decreasing ?
A graphical sketch might help.
number-theory analytic-number-theory riemann-zeta
number-theory analytic-number-theory riemann-zeta
edited Nov 29 at 19:55
asked Nov 29 at 19:36
user507152
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It doesn't follow that $lvert zeta(1/2 + it) rvert$ is strictly increasing or decreasing.
In fact, since $lvert zeta(1/2 + it)rvert = lvert zeta(1/2 - it) rvert$ from the functional equation, one cannot have that $lvert zeta(1/2 + it) rvert$ is strictly increasing or decreasing at $0$, since the function is symmetric there.
One can plot this readily using something like sage, or something online like wolfram alpha. You get the following plot.
answered Nov 29 at 19:54
davidlowryduda♦
74.3k7117251
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It doesn't follow that $lvert zeta(1/2 + it) rvert$ is strictly increasing or decreasing.
In fact, since $lvert zeta(1/2 + it)rvert = lvert zeta(1/2 - it) rvert$ from the functional equation, one cannot have that $lvert zeta(1/2 + it) rvert$ is strictly increasing or decreasing at $0$, since the function is symmetric there.
One can plot this readily using something like sage, or something online like wolfram alpha. You get the following plot.
answered Nov 29 at 19:54
davidlowryduda♦
74.3k7117251
add a comment |
It doesn't follow that $lvert zeta(1/2 + it) rvert$ is strictly increasing or decreasing.
In fact, since $lvert zeta(1/2 + it)rvert = lvert zeta(1/2 - it) rvert$ from the functional equation, one cannot have that $lvert zeta(1/2 + it) rvert$ is strictly increasing or decreasing at $0$, since the function is symmetric there.
One can plot this readily using something like sage, or something online like wolfram alpha. You get the following plot.
answered Nov 29 at 19:54
davidlowryduda♦
74.3k7117251
add a comment |
It doesn't follow that $lvert zeta(1/2 + it) rvert$ is strictly increasing or decreasing.
In fact, since $lvert zeta(1/2 + it)rvert = lvert zeta(1/2 - it) rvert$ from the functional equation, one cannot have that $lvert zeta(1/2 + it) rvert$ is strictly increasing or decreasing at $0$, since the function is symmetric there.
One can plot this readily using something like sage, or something online like wolfram alpha. You get the following plot.
answered Nov 29 at 19:54
davidlowryduda♦
74.3k7117251
It doesn't follow that $lvert zeta(1/2 + it) rvert$ is strictly increasing or decreasing.
In fact, since $lvert zeta(1/2 + it)rvert = lvert zeta(1/2 - it) rvert$ from the functional equation, one cannot have that $lvert zeta(1/2 + it) rvert$ is strictly increasing or decreasing at $0$, since the function is symmetric there.
One can plot this readily using something like sage, or something online like wolfram alpha. You get the following plot.
answered Nov 29 at 19:54
davidlowryduda♦
74.3k7117251
edited Nov 29 at 20:03
answered Nov 29 at 19:54
davidlowryduda♦
74.3k7117251
answered Nov 29 at 19:54
davidlowryduda♦
74.3k7117251
answered Nov 29 at 19:54
davidlowryduda♦
74.3k7117251
74.3k7117251
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