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Francis Brown Theorem says that $\zeta(a_{1},\dots ,a_{r})$ the multi-zeta value of weight $N=a_{1}+\dots +a_{r}$ is a $\mathbb{Q}$-linear combination of elements of the set $S=\{\zeta(a_{1},\dots, a_{n})| \text{for any i, } a_{i}\in\{2,3\} \text{ and } a_{1}+\dots +a_{n}=N \}$

What I don't understand in the statement is the following: are the elements of $S$ $\mathbb{Q}$-linearly independent?

I read that there is a surprising $\mathbb{Q}$-linear relation between some values of the multi-zeta function $\zeta$ of weight 12. The relation I'm talking about is the following: $$28\zeta(3,9)+ 150\zeta(5,7)+168\zeta(7,5)= \frac{5197}{691}\zeta(12) $$ Does this relation have some arithmetic-geometric interpretation ?

In his talk (around 5:50) F. Brown made a remark by saying that the relation above relation is related to cusps forms for $SL(2,\mathbb{Z})$. What that means exactly and what is the relation between cusps forms and the $\mathbb{Q}$-linear relation above ?

Francis Brown Theorem says that $\zeta(a_{1},\dots ,a_{r})$ the multi-zeta value of weight $N=a_{1}+\dots +a_{r}$ is a $\mathbb{Q}$-linear combination of elements of the set $S=\{\zeta(a_{1},\dots, a_{n})| \text{for any i, } a_{i}\in\{2,3\} \text{ and } a_{1}+\dots +a_{n}=N \}$

What I don't understand in the statement is the following: are the elements of $S$ $\mathbb{Q}$-linearly independent?

I read that there is a surprising $\mathbb{Q}$-linear relation between some values of the multi-zeta function $\zeta$ of weight 12. The relation I'm talking about is the following: $$28\zeta(3,9)+ 150\zeta(5,7)+168\zeta(7,5)= \frac{5197}{691}\zeta(12) $$ Does this relation have some arithmetic-geometric interpretation ?

In his talk (around 5:50) F. Brown made a remark by saying that the relation above relation is related to cusp forms for $SL(2,\mathbb{Z})$. What that means exactly and what is the relation between cusps forms and the $\mathbb{Q}$-linear relation above ?

Francis Brown Theorem says that $\zeta(a_{1},\dots ,a_{r})$ the multi-zeta value of weight $N=a_{1}+\dots +a_{r}$ is a $\mathbb{Q}$-linear combination of elements of the set $S=\{\zeta(a_{1},\dots, a_{n})| \text{for any i, } a_{i}\in\{2,3\} \text{ and } a_{1}+\dots +a_{n}=N \}$

What I don't understand in the statement is the following: are the elements of $S$ $\mathbb{Q}$-linearly independent?

I read that there is a surprising $\mathbb{Q}$-linear relation between some values of the multi-zeta function $\zeta$ of weight 12. The relation I'm talking about is the following: $$28\zeta(3,9)+ 150\zeta(5,7)+168\zeta(7,5)= \frac{5197}{691}\zeta(12) $$ Does this relation have some arithmetic-geometric interpretation ?

In his talk (around 5:50) F. Brown made a remark by saying that the about relation is related to cusps forms for $SL(2,\mathbb{Z})$. What that means exactly and what is the relation between cusps forms and the $\mathbb{Q}$-linear relation above ?

Francis Brown Theorem says that $\zeta(a_{1},\dots ,a_{r})$ the multi-zeta value of weight $N=a_{1}+\dots +a_{r}$ is a $\mathbb{Q}$-linear combination of elements of the set $S=\{\zeta(a_{1},\dots, a_{n})| \text{for any i, } a_{i}\in\{2,3\} \text{ and } a_{1}+\dots +a_{n}=N \}$

What I don't understand in the statement is the following: are the elements of $S$ $\mathbb{Q}$-linearly independent?

I read that there is a surprising $\mathbb{Q}$-linear relation between some values of the multi-zeta function $\zeta$ of weight 12. The relation I'm talking about is the following: $$28\zeta(3,9)+ 150\zeta(5,7)+168\zeta(7,5)= \frac{5197}{691}\zeta(12) $$ Does this relation have some arithmetic-geometric interpretation ?

In his talk (around 5:50) F. Brown made a remark by saying that the relation above relation is related to cusps forms for $SL(2,\mathbb{Z})$. What that means exactly and what is the relation between cusps forms and the $\mathbb{Q}$-linear relation above ?

Francis Brown Theorem says that $\zeta(a_{1},\dots ,a_{r})$ the multi-zeta value of weight $N=a_{1}+\dots +a_{r}$ is a $\mathbb{Q}$-linear combination of elements of the set $S=\{\zeta(a_{1},\dots, a_{n})| \text{for any i, } a_{i}\in\{2,3\} \text{ and } a_{1}+\dots +a_{n}=N \}$

What I don't understand in the statement is the following: are the elements of $S$ $\mathbb{Q}$-linearly independent?

I read that there is a surprising $\mathbb{Q}$-linear relation between some values of the multi-zeta function $\zeta$ of weight 12. The relation I'm talking about is the following: $$28\zeta(3,9)+ 150\zeta(5,7)+168\zeta(7,5)= \frac{5197}{691}\zeta(12) $$ Does this relation have some arithmetic-geometric interpretation ?

Francis Brown Theorem says that $\zeta(a_{1},\dots ,a_{r})$ the multi-zeta value of weight $N=a_{1}+\dots +a_{r}$ is a $\mathbb{Q}$-linear combination of elements of the set $S=\{\zeta(a_{1},\dots, a_{n})| \text{for any i, } a_{i}\in\{2,3\} \text{ and } a_{1}+\dots +a_{n}=N \}$

What I don't understand in the statement is the following: are the elements of $S$ $\mathbb{Q}$-linearly independent?

I read that there is a surprising $\mathbb{Q}$-linear relation between some values of the multi-zeta function $\zeta$ of weight 12. The relation I'm talking about is the following: $$28\zeta(3,9)+ 150\zeta(5,7)+168\zeta(7,5)= \frac{5197}{691}\zeta(12) $$ Does this relation have some arithmetic-geometric interpretation ?

In his talk (around 5:50) F. Brown made a remark by saying that the about relation is related to cusps forms for $SL(2,\mathbb{Z})$. What that means exactly and what is the relation between cusps forms and the $\mathbb{Q}$-linear relation above ?