I need to compute a set of multivariate definite integrals with infinite integration domain $$\displaystyle \int_{-\infty}^{\infty} \cdots \int_{-\infty}^{\infty} f(x_1,x_2, \ldo …

When do the notions of totally disconnected space and zero-dimensional space coincide? From what I gather, there are at least three common notions of topological dimension: coverin …

Given a set of distances between every pair of points of an integral point set P of n points; say D = {${d_i}$} Q1. What is the least time complexity possible/known for …

Let me begin with an example. Consider the computable function $f(x) = 2x$. A Turing machine can implement this function in $O(|n|)$ steps: simply walk to the end of the input st …

Let $R$ be a (commutative) noetherian integral domain. Let $I$ be a prime ideal of $R$. Let $S$ be a finitely generated $R$-subalgebra of $\mathrm{Frac}(R)$. Is $S \cap R_I$ nece …

Suppose I have a collection of "elements" together with operations that satisfy the axioms for a commutative ring with identity --- except that these elements form not a set, but a …

How can I prove, that for any positive integer $n>0$ there is a prime $p$, such that the multiplicative group of the residue ring $Z_p^*$ contains an element $a$ of order $n$? No i …

Offhand I can think of two ways in classical homotopy theory: Show that $\pi_k(S^n)=0$ for $k\lt n$ by deforming a map $S^k\to S^n$ to be non-surjective, then contracting it away …

Let $PB_n$ be the pure braid group on $n$ strands. The group $PB_n$ has every conceivable finiteness property. Also, it has a large abelianization. My question is whether the co …

Let $C$ be a smooth curve over a finite field of characteristic $p$. Let $t$ be a local parameter at a point. If $f$ is a regular function on a neighbourhood of the point, one can …

If X distributed as Γ(a,σx) and Y distributed as Γ(b,σy). What will be the probability density function of R? Where R=X/Y+C, here C is a positive constant, Γ(.,.) denotes standard …

Let $F:A\to A'$ be a (full) exact embedding of abelian categories. When $D(F):D(A)\to D(A')$ (or its bounded version) is a full embedding also? I would be interested in any neces …

Suppose to have $\phi$ a ring morphsim from $A$ to $B$, let $X=SpecA$ , $Y=SpecB$ and $\psi$ the induced morphism of affine schemes. It's true that if $\psi$ dominant than $\phi$ …

Let $D$ be a totally definite quaternion algebra over a totally real number field $F$. Let $U$ be an open compact subgroup of $D(\mathbb{A}_F)^\times$, maximal compact almost every …

Background: This question is related to a proof offered by Gian Maria Dall'Ara. In Ways to prove the fundamental theorem of algebra (FTA), he formulates the FTA as: Every c …