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Removed the word ponent, that seems a bad translation from the Spanish word "ponente"
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Here $s=\sigma+it$ denotes the complex variable. We denote the Ramanujan's zeta function $$\varphi(s)=\sum_{n=1}^\infty\frac{\tau(n)}{n^s}$$

for $\Re(s)>7$, where $\tau(n)$ is the Ramanujan tau function.

While I was studying a video by Harper, a video from YouTube with title The Riemann zeta function in short intervals - Harper - Bourbaki - 30/03/19 from the official channel Institut Henri Poincaré, I wondered if a similar principle than the ponentprofessor shows as Principle I (see also PRINCIPLE 1.3 from [2]) works in some suitable sense for the Ramanujan's zeta function $\varphi(s)$.

Principle. For any $s$ with $\Re(s)\geq \frac{11}{6}$ (or at least $\Re(s)> \frac{11}{6}$) and $|\Im(s)|\geq 1$ we have $$\varphi(s)\cdot\prod_{\substack{p\text{ prime }\\p\leq X(s)}}\left(1-\frac{\tau(p)}{p^s}+\frac{p^{11}}{p^{2s}}\right)\simeq 1\tag{1}$$ in some "suitable sense".

Question. Does previous Principle involving the identity $(1)$ work for any suitable sense? Explain your words. Many thanks.

Thus I am asking about the explanation of the meaning of previous Principle involving the identity $(1)$. I just wrote it as a similar statement than the Principle I from Harper's colloquium (at few first minutes of the colloquium), but I have no knowledges to know the meaning of it.

References:

[1] G. H. Hardy, Ramanujan: Twelve lectures on subjects suggested by his life and work, AMS Chelsea Publishing (2002).

[2] Adam J. Harper, The Riemann zeta function in short intervals [after Najnudel, and Arguin, Belius, Bourgade, Radziwiłł, and Soundararajan], Séminaire BOURBAKI, 71e année, 2018–2019, no 1159 (Mars 2019).

Here $s=\sigma+it$ denotes the complex variable. We denote the Ramanujan's zeta function $$\varphi(s)=\sum_{n=1}^\infty\frac{\tau(n)}{n^s}$$

for $\Re(s)>7$, where $\tau(n)$ is the Ramanujan tau function.

While I was studying a video by Harper, a video from YouTube with title The Riemann zeta function in short intervals - Harper - Bourbaki - 30/03/19 from the official channel Institut Henri Poincaré, I wondered if a similar principle than the ponent shows as Principle I (see also PRINCIPLE 1.3 from [2]) works in some suitable sense for the Ramanujan's zeta function $\varphi(s)$.

Principle. For any $s$ with $\Re(s)\geq \frac{11}{6}$ (or at least $\Re(s)> \frac{11}{6}$) and $|\Im(s)|\geq 1$ we have $$\varphi(s)\cdot\prod_{\substack{p\text{ prime }\\p\leq X(s)}}\left(1-\frac{\tau(p)}{p^s}+\frac{p^{11}}{p^{2s}}\right)\simeq 1\tag{1}$$ in some "suitable sense".

Question. Does previous Principle involving the identity $(1)$ work for any suitable sense? Explain your words. Many thanks.

Thus I am asking about the explanation of the meaning of previous Principle involving the identity $(1)$. I just wrote it as a similar statement than the Principle I from Harper's colloquium (at few first minutes of the colloquium), but I have no knowledges to know the meaning of it.

References:

[1] G. H. Hardy, Ramanujan: Twelve lectures on subjects suggested by his life and work, AMS Chelsea Publishing (2002).

[2] Adam J. Harper, The Riemann zeta function in short intervals [after Najnudel, and Arguin, Belius, Bourgade, Radziwiłł, and Soundararajan], Séminaire BOURBAKI, 71e année, 2018–2019, no 1159 (Mars 2019).

Here $s=\sigma+it$ denotes the complex variable. We denote the Ramanujan's zeta function $$\varphi(s)=\sum_{n=1}^\infty\frac{\tau(n)}{n^s}$$

for $\Re(s)>7$, where $\tau(n)$ is the Ramanujan tau function.

While I was studying a video by Harper, a video from YouTube with title The Riemann zeta function in short intervals - Harper - Bourbaki - 30/03/19 from the official channel Institut Henri Poincaré, I wondered if a similar principle than the professor shows as Principle I (see also PRINCIPLE 1.3 from [2]) works in some suitable sense for the Ramanujan's zeta function $\varphi(s)$.

Principle. For any $s$ with $\Re(s)\geq \frac{11}{6}$ (or at least $\Re(s)> \frac{11}{6}$) and $|\Im(s)|\geq 1$ we have $$\varphi(s)\cdot\prod_{\substack{p\text{ prime }\\p\leq X(s)}}\left(1-\frac{\tau(p)}{p^s}+\frac{p^{11}}{p^{2s}}\right)\simeq 1\tag{1}$$ in some "suitable sense".

Question. Does previous Principle involving the identity $(1)$ work for any suitable sense? Explain your words. Many thanks.

Thus I am asking about the explanation of the meaning of previous Principle involving the identity $(1)$. I just wrote it as a similar statement than the Principle I from Harper's colloquium (at few first minutes of the colloquium), but I have no knowledges to know the meaning of it.

References:

[1] G. H. Hardy, Ramanujan: Twelve lectures on subjects suggested by his life and work, AMS Chelsea Publishing (2002).

[2] Adam J. Harper, The Riemann zeta function in short intervals [after Najnudel, and Arguin, Belius, Bourgade, Radziwiłł, and Soundararajan], Séminaire BOURBAKI, 71e année, 2018–2019, no 1159 (Mars 2019).

Fixed typo and grammar
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Here $s=\sigma+it$ denotes the complex variable. We denote the Ramanujan's zeta function $$\varphi(n)=\sum_{n=1}^\infty\frac{\tau(n)}{n^s}$$$$\varphi(s)=\sum_{n=1}^\infty\frac{\tau(n)}{n^s}$$

for $\Re(s)>7$, where $\tau(n)$ is the Ramanujan tau function.

While I was studying a video by Harper, a video from YouTube with title The Riemann zeta function in short intervals - Harper - Bourbaki - 30/03/19 from the official channel Institut Henri Poincaré, I wondered if a similar principle than the ponent shows as Principle I (see also PRINCIPLE 1.3 from [2]) works in some suitable sense for the Ramanujan's zeta function $\varphi(s)$.

Principle. For any $s$ with $\Re(s)\geq \frac{11}{6}$ (or at least $\Re(s)> \frac{11}{6}$) and $|\Im(s)|\geq 1$ we have $$\varphi(s)\cdot\prod_{\substack{p\text{ prime }\\p\leq X(s)}}\left(1-\frac{\tau(p)}{p^s}+\frac{p^{11}}{p^{2s}}\right)\simeq 1\tag{1}$$ in some "suitable sense".

Question. Does previous Principle involving the identity $(1)$ make sensework for any suitable sense? Explain your words. Many thanks.

Thus I am asking about the explanation of the meaning of previous Principle involving the identity $(1)$. I just wrote it as a similar statement than the Principle I from Harper's colloquium (at few first minutes of the colloquium), but I have no knowledges to know the meaning of it.

References:

[1] G. H. Hardy, Ramanujan: Twelve lectures on subjects suggested by his life and work, AMS Chelsea Publishing (2002).

[2] Adam J. Harper, The Riemann zeta function in short intervals [after Najnudel, and Arguin, Belius, Bourgade, Radziwiłł, and Soundararajan], Séminaire BOURBAKI, 71e année, 2018–2019, no 1159 (Mars 2019).

Here $s=\sigma+it$ denotes the complex variable. We denote the Ramanujan's zeta function $$\varphi(n)=\sum_{n=1}^\infty\frac{\tau(n)}{n^s}$$

for $\Re(s)>7$, where $\tau(n)$ is the Ramanujan tau function.

While I was studying a video by Harper, a video from YouTube with title The Riemann zeta function in short intervals - Harper - Bourbaki - 30/03/19 from the official channel Institut Henri Poincaré, I wondered if a similar principle than the ponent shows as Principle I (see also PRINCIPLE 1.3 from [2]) works in some suitable sense for the Ramanujan's zeta function $\varphi(s)$.

Principle. For any $s$ with $\Re(s)\geq \frac{11}{6}$ (or at least $\Re(s)> \frac{11}{6}$) and $|\Im(s)|\geq 1$ we have $$\varphi(s)\cdot\prod_{\substack{p\text{ prime }\\p\leq X(s)}}\left(1-\frac{\tau(p)}{p^s}+\frac{p^{11}}{p^{2s}}\right)\simeq 1\tag{1}$$ in some "suitable sense".

Question. Does previous Principle involving the identity $(1)$ make sense for any suitable sense? Explain your words. Many thanks.

Thus I am asking about the explanation of the meaning of previous Principle involving the identity $(1)$. I just wrote it as a similar statement than the Principle I from Harper's colloquium (at few first minutes of the colloquium), but I have no knowledges to know the meaning of it.

References:

[1] G. H. Hardy, Ramanujan: Twelve lectures on subjects suggested by his life and work, AMS Chelsea Publishing (2002).

[2] Adam J. Harper, The Riemann zeta function in short intervals [after Najnudel, and Arguin, Belius, Bourgade, Radziwiłł, and Soundararajan], Séminaire BOURBAKI, 71e année, 2018–2019, no 1159 (Mars 2019).

Here $s=\sigma+it$ denotes the complex variable. We denote the Ramanujan's zeta function $$\varphi(s)=\sum_{n=1}^\infty\frac{\tau(n)}{n^s}$$

for $\Re(s)>7$, where $\tau(n)$ is the Ramanujan tau function.

While I was studying a video by Harper, a video from YouTube with title The Riemann zeta function in short intervals - Harper - Bourbaki - 30/03/19 from the official channel Institut Henri Poincaré, I wondered if a similar principle than the ponent shows as Principle I (see also PRINCIPLE 1.3 from [2]) works in some suitable sense for the Ramanujan's zeta function $\varphi(s)$.

Principle. For any $s$ with $\Re(s)\geq \frac{11}{6}$ (or at least $\Re(s)> \frac{11}{6}$) and $|\Im(s)|\geq 1$ we have $$\varphi(s)\cdot\prod_{\substack{p\text{ prime }\\p\leq X(s)}}\left(1-\frac{\tau(p)}{p^s}+\frac{p^{11}}{p^{2s}}\right)\simeq 1\tag{1}$$ in some "suitable sense".

Question. Does previous Principle involving the identity $(1)$ work for any suitable sense? Explain your words. Many thanks.

Thus I am asking about the explanation of the meaning of previous Principle involving the identity $(1)$. I just wrote it as a similar statement than the Principle I from Harper's colloquium (at few first minutes of the colloquium), but I have no knowledges to know the meaning of it.

References:

[1] G. H. Hardy, Ramanujan: Twelve lectures on subjects suggested by his life and work, AMS Chelsea Publishing (2002).

[2] Adam J. Harper, The Riemann zeta function in short intervals [after Najnudel, and Arguin, Belius, Bourgade, Radziwiłł, and Soundararajan], Séminaire BOURBAKI, 71e année, 2018–2019, no 1159 (Mars 2019).

Fixed a typo
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user142929
user142929
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Here $s=\sigma+it$ denotes the complex variable. We denote the Ramanujan's zeta function $$\varphi(n)=\sum_{n=1}^\infty\frac{\tau(n)}{n^s}$$

for $\Re(s)>7$, where $\tau(n)$ is the Ramanujan tau function.

While I was studying a video by Harper, a video from YouTube with title The Riemann zeta function in short intervals - Harper - Bourbaki - 30/03/19 from the official channel Institut Henri Poincaré, I wondered if a similar principle than the ponent shows as Principle I (see also PRINCIPLE 1.3 from [2]) works in some suitable sense for the Ramanujan's zeta function $\varphi(s)$.

Principle. For any $s$ with $\Re(s)\geq \frac{11}{6}$ (or at least $\Re(s)> \frac{11}{6}$) and $|\Im(s)|\geq 1$ we have $$\varphi(n)\cdot\prod_{\substack{p\text{ prime }\\p\leq X(s)}}\left(1-\frac{\tau(p)}{p^s}+\frac{p^{11}}{p^{2s}}\right)\simeq 1\tag{1}$$$$\varphi(s)\cdot\prod_{\substack{p\text{ prime }\\p\leq X(s)}}\left(1-\frac{\tau(p)}{p^s}+\frac{p^{11}}{p^{2s}}\right)\simeq 1\tag{1}$$ in some "suitable sense".

Question. Does previous Principle involving the identity $(1)$ make sense for any suitable sense? Explain your words. Many thanks.

Thus I am asking about the explanation of the meaning of previous Principle involving the identity $(1)$. I just wrote it as a similar statement than the Principle I from Harper's colloquium (at few first minutes of the colloquium), but I have no knowledges to know the meaning of it.

References:

[1] G. H. Hardy, Ramanujan: Twelve lectures on subjects suggested by his life and work, AMS Chelsea Publishing (2002).

[2] Adam J. Harper, The Riemann zeta function in short intervals [after Najnudel, and Arguin, Belius, Bourgade, Radziwiłł, and Soundararajan], Séminaire BOURBAKI, 71e année, 2018–2019, no 1159 (Mars 2019).

Here $s=\sigma+it$ denotes the complex variable. We denote the Ramanujan's zeta function $$\varphi(n)=\sum_{n=1}^\infty\frac{\tau(n)}{n^s}$$

for $\Re(s)>7$, where $\tau(n)$ is the Ramanujan tau function.

While I was studying a video by Harper, a video from YouTube with title The Riemann zeta function in short intervals - Harper - Bourbaki - 30/03/19 from the official channel Institut Henri Poincaré, I wondered if a similar principle than the ponent shows as Principle I (see also PRINCIPLE 1.3 from [2]) works in some suitable sense for the Ramanujan's zeta function $\varphi(s)$.

Principle. For any $s$ with $\Re(s)\geq \frac{11}{6}$ (or at least $\Re(s)> \frac{11}{6}$) and $|\Im(s)|\geq 1$ we have $$\varphi(n)\cdot\prod_{\substack{p\text{ prime }\\p\leq X(s)}}\left(1-\frac{\tau(p)}{p^s}+\frac{p^{11}}{p^{2s}}\right)\simeq 1\tag{1}$$ in some "suitable sense".

Question. Does previous Principle involving the identity $(1)$ make sense for any suitable sense? Explain your words. Many thanks.

Thus I am asking about the explanation of the meaning of previous Principle involving the identity $(1)$. I just wrote it as a similar statement than the Principle I from Harper's colloquium (at few first minutes of the colloquium), but I have no knowledges to know the meaning of it.

References:

[1] G. H. Hardy, Ramanujan: Twelve lectures on subjects suggested by his life and work, AMS Chelsea Publishing (2002).

[2] Adam J. Harper, The Riemann zeta function in short intervals [after Najnudel, and Arguin, Belius, Bourgade, Radziwiłł, and Soundararajan], Séminaire BOURBAKI, 71e année, 2018–2019, no 1159 (Mars 2019).

Here $s=\sigma+it$ denotes the complex variable. We denote the Ramanujan's zeta function $$\varphi(n)=\sum_{n=1}^\infty\frac{\tau(n)}{n^s}$$

for $\Re(s)>7$, where $\tau(n)$ is the Ramanujan tau function.

While I was studying a video by Harper, a video from YouTube with title The Riemann zeta function in short intervals - Harper - Bourbaki - 30/03/19 from the official channel Institut Henri Poincaré, I wondered if a similar principle than the ponent shows as Principle I (see also PRINCIPLE 1.3 from [2]) works in some suitable sense for the Ramanujan's zeta function $\varphi(s)$.

Principle. For any $s$ with $\Re(s)\geq \frac{11}{6}$ (or at least $\Re(s)> \frac{11}{6}$) and $|\Im(s)|\geq 1$ we have $$\varphi(s)\cdot\prod_{\substack{p\text{ prime }\\p\leq X(s)}}\left(1-\frac{\tau(p)}{p^s}+\frac{p^{11}}{p^{2s}}\right)\simeq 1\tag{1}$$ in some "suitable sense".

Question. Does previous Principle involving the identity $(1)$ make sense for any suitable sense? Explain your words. Many thanks.

Thus I am asking about the explanation of the meaning of previous Principle involving the identity $(1)$. I just wrote it as a similar statement than the Principle I from Harper's colloquium (at few first minutes of the colloquium), but I have no knowledges to know the meaning of it.

References:

[1] G. H. Hardy, Ramanujan: Twelve lectures on subjects suggested by his life and work, AMS Chelsea Publishing (2002).

[2] Adam J. Harper, The Riemann zeta function in short intervals [after Najnudel, and Arguin, Belius, Bourgade, Radziwiłł, and Soundararajan], Séminaire BOURBAKI, 71e année, 2018–2019, no 1159 (Mars 2019).

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