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Tokita Ohma
Tokita Ohma
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Zeros of the $m$th derivative of $\xi$

In his paper on Zeros of derivatives of Riemann $\xi$-function on critical line Brian Conrey mention that

It can be shown that the Riemann hypothesis implies that all zeros of $\xi^m (s)$$\xi (s)$, the $m$th derivative of $\xi$-function, have real part $1/2$ for any $m$. Where $$\xi(s)=\frac{1}{2}s(s-1)\pi^{-s/2}\Gamma\bigg(\frac{s}{2}\bigg) \zeta(s).$$

Could anyone kindly recommend some references, books, or scholarly articles that elaborate on this topic? I would greatly appreciate your assistance. Thank you in anticipation!

Zeros of the $m$th derivative of $\xi$

In his paper on Zeros of derivatives of Riemann $\xi$-function on critical line Brian Conrey mention that

It can be shown that the Riemann hypothesis implies that all zeros of $\xi^m (s)$, the $m$th derivative of $\xi$-function, have real part $1/2$ for any $m$. Where $$\xi(s)=\frac{1}{2}s(s-1)\pi^{-s/2}\Gamma\bigg(\frac{s}{2}\bigg) \zeta(s).$$

Could anyone kindly recommend some references, books, or scholarly articles that elaborate on this topic? I would greatly appreciate your assistance. Thank you in anticipation!

Zeros of the derivative of $\xi$

In his paper on Zeros of derivatives of Riemann $\xi$-function on critical line Brian Conrey mention that

It can be shown that the Riemann hypothesis implies that all zeros of $\xi (s)$, the derivative of $\xi$-function, have real part $1/2$ for any $m$. Where $$\xi(s)=\frac{1}{2}s(s-1)\pi^{-s/2}\Gamma\bigg(\frac{s}{2}\bigg) \zeta(s).$$

Could anyone kindly recommend some references, books, or scholarly articles that elaborate on this topic? I would greatly appreciate your assistance. Thank you in anticipation!

Source Link
Tokita Ohma
Tokita Ohma
  • 61
  • 2

Zeros of the $m$th derivative of $\xi$

In his paper on Zeros of derivatives of Riemann $\xi$-function on critical line Brian Conrey mention that

It can be shown that the Riemann hypothesis implies that all zeros of $\xi^m (s)$, the $m$th derivative of $\xi$-function, have real part $1/2$ for any $m$. Where $$\xi(s)=\frac{1}{2}s(s-1)\pi^{-s/2}\Gamma\bigg(\frac{s}{2}\bigg) \zeta(s).$$

Could anyone kindly recommend some references, books, or scholarly articles that elaborate on this topic? I would greatly appreciate your assistance. Thank you in anticipation!