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Apr
27
comment How do I find an upper bound on $z/(z^3+1)$ on a circular path with radius R centred at the origin?
Why not let $z=Re^{2\pi it}$ and work with the real variable $t\in[0,1]$?
Apr
17
comment Counterexample to distance between two disjoint compact manifolds always great than some positive real number
The point $(1,1)$ is not in the graph of $f$ but it is not an inner point in its complement set. Thus the graph of $f$ is not closed
Apr
14
awarded  number-theory
Apr
13
awarded  ring-theory
Apr
7
comment Demystifying modular forms
@user929304: I can just hope that you'll grow to see this deep richness more as a motivation than a put-off.
Apr
7
comment Demystifying modular forms
@user929304: I understand your feelings which have been shared by everyone's first contacts with higher mathematics. Modular forms are a rich and deep theory that sits at the crossroad of many important branches of mathematics. The complex analytic approach is certainly the most elementary but, in some sense, the most obscure since many properties appear casual, somewhat artificial and overall magic. To appreciate the other points of view (where for instance the role of higher arithmetic becomes paramount) some general knowledge of other mathematical theories is required.
Apr
6
comment Demystifying modular forms
@user929304: About (b), the automorphic factor $(cz+d)^k$ is a cocycle that allows to regard modular forms as (holomorphic) global sections of certain line bundles over the Riemann surfaces obtained taking the quotient of $\cal H$ by (subgroups of) the modular group. I had formulated (d) incorrectly and edited now, but in general if you have a space $X$ acted upon by a group $\Gamma$ you may consider the space of orbits $\Gamma\backslash X$ which under some conditions on the action will be "as nice as" $X$.
Apr
6
revised Demystifying modular forms
added 125 characters in body
Apr
6
comment Area of a circle $\pi r^2$
It wasn't the Greeks to find that the circle couldn't be squared (of course one should explain what that means...) but it was eventually proved only in the second half of the 19th century.
Apr
6
answered Demystifying modular forms
Apr
5
answered What is $\displaystyle\int_{2}^{2}\frac{dx}{x-2}$?
Apr
5
comment Character regular representation
@thinker: If $V$ is just any representation, what is $X(1_G)$ where $X$ is the character of $V$?
Apr
4
reviewed Leave Open Finite dimensional division ring over an algebraically closed field
Apr
4
reviewed Leave Open Prove this is a tautology with logical equivalence laws only.
Apr
4
reviewed Leave Open Proof help number theory
Apr
4
reviewed Leave Open Why is it more efficient to compute the modular exponentiation by calculating to the power of two and not three for example?
Apr
4
answered Construction of Tensor Product on $\mathbb R^2$
Apr
4
answered Character regular representation
Apr
3
awarded  elementary-number-theory
Apr
2
awarded  Nice Answer