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$123456789 \times x$=
What can $x$ be to give an obvious answer?
I have got $0,1,10,10^n$ for integer n, $\pi$ and all the above mltiply by $i$ will also be an obvious answer.
Are there any other solutions?
Any help/contribution appreciated.
Note: $\pi$ works because you must give an exact an...
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I read about how Hecke groups are a particular generalisation of the modular group, generalising one of the generators of the modular group to $z\mapsto z + \lambda$. Have people studied generalisations of the other generator of the modular group, perhaps generalising to $z \mapsto \dfrac{-1}{z^n...
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The modular group $PSL_2(\mathbb{Z})$ acts on the hyperbolic half-space $H$ by
$$h\cdot z=\frac{az+b}{cz+d},\;z\in H,\;h=\begin{pmatrix}a&b\\c&d\end{pmatrix}\in PSL_2(\mathbb{Z})$$
with $ad-bc=1$. The modular group is generated by two elements $S$ and $T$ such that
$$S^2=(ST)^3=1,$$
where we can ...
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Let $\Gamma$ be a finite index subgroup of $\Gamma(1)=SL_2(\mathbf{Z})$ and $f$ a modular function for $\Gamma$. By this I mean a meromorphic function defined on the upper half-plane $f: \mathfrak{h} \to \mathbf{C}$, satisfying a growth condition at infinity, which is invariant by $\Gamma$: for e...
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In mathematics, the modular group is the projective special linear group PSL(2,Z) of 2 x 2 matrices with integer coefficients and unit determinant. The matrices A and -A are identified. The modular group acts on the upper-half of the complex plane by fractional linear transformations, and the name "modular group" comes from the relation to moduli spaces and not from modular arithmetic.
== Definition ==
The modular group Γ is the group of linear fractional transformations of the upper half of the complex plane which have the form
z
↦
...
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Let $\mathbb{K}$ be a field and $A$ a finite dimensional $\mathbb{k}$-algebra with identity $1_{A}$. For two $A$-modules $M$ and $N$ we have the set of all $A$-linear maps from $M$ to $N$ denoted $\mathrm{Hom}_{A}(M,N)$. This set is not in general an $A$-module neither by the left nor by the righ...
In the book of Analysis On Manifolds by Munkres, at page 141, it is given that
However, I think there is a problem in the existence such an $M$.
Reason:
Because we do know that the supports of $\phi_i$s, i.e $S_i$s, will form a cover for $A$, and hence for $D$, but by the compactness of $D$,...
The tag calculus-identities has been created about a year ago in this question: Quotient rule/Quotient rule.
When I look at questions which have this tag now or which were tagged with this tag in the past, it seems that people are using it for all sorts of stuff. (Basically anything where some ...
