The von Staudt-Clausen theorem expresses that the Bernoulli numbers' denominators have a very special form (see the wikipedia page on the theorem for more details). What interests …

I was going through the proof of Stickelberger's Theorem, as given in the book 'Algebraic Number Theory' by Richard A Mollin, and I am having some problem in understanding the proo …

If we have a complex Morse function on a complex four-manifold, $f: X\to \mathbb{C} $, can we tell from the function how the genus of inverse images $f^{-1}(z)$ (for regular values …

I am trying to write a computer program which computes the action of the exponential of a differential operator on a function, for any given differential operator. Examples: $\ex …

For me second-countability always felt like to be the more important and fundamental concept from general topology than separability. I wonder whether there are any points which ca …

Hello all, This is a question that might or might not be related to my previous one. Imagine you have two matrices: Matrix $\mathbf{\Phi}=[\Phi_1,\ldots,\Phi_M]\in\mathbb{R}^{L …

The background of my question comes from an observation that what we teach in schools does not always reflect what we practice. Beauty is part of what drives mathematicians, but w …

What are the necessary and sufficient conditions for two finite groups $G$ and $H$ to have same complex-valued character table? Is there any criterion for which one could know abou …

After Jun-Ichi Igusa' talk at ICM 1962, H.J. Tramer computed the ring structure of the integral cohomology of such a space ( not yet called WPS ). In 1971 M.F. Atiyah called it W …

After Jun-Ichi Igusa' talk at ICM 1962, H.J. Tramer computed the ring structure of the integral cohomology of such a space ( not yet called WPS ). In 1971 M.F. Atiyah called it W …

Suppose that you have decomposed a manifold $M$ into cells (I care most, if it matters, about compact oriented smooth manifolds; but if my question can be solved in the PL category …

Dear colleagues, Could you give me a reference (not a proof:) to the following folklore result. If $X\subset\mathbb P^n$ is a smooth irreducible projective variety of dimension $ …

Hi all, I have a cube, sized 39 x 13 x 8. I need to find out how many of them can fit in a cube of 100 x 100 x 100. I need to find the highest number possible. Do you know of a w …

I would like to know the ring structure of $K(Q_n)$ explicitly where $Q_n \subset \mathbb{P}^{n+1}$ is the non-singular $n$-dimensional complex quadric and $K(Q_n) = K^0(Q_n)$ is …

Perhaps the "proofs" of ABC conjecture or newly released weak version of twin prime conjecture or alike readily come to your mind. These are not the proofs I am looking for. Indeed …