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# MathOverflow : Recent Questions and Answers

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## What are some good resources for mathematical translation?

I am currently in the process of translating a lecture on the étale topology by John Hubbard from French into English (and from transparencies into Beamer). For the most...

Asked on 01/05/2022 by Matt Noonan

## Inequality for hook numbers in Young diagrams

Consider a Young diagram $lambda = (lambda_1,ldots,lambda_ell)$. For a square $(i,j) in lambda$, define hook numbers $h_{ij} = lambda_i + lambda_j' -i - j +1$ and...

Asked on 01/05/2022 by Igor Pak

Let $V_1,ldots , V_k$ be vector spaces of dimensions $n_1,ldots , n_k$ over a field of characteristic zero. Consider the rational map$newcommand{PP}{mathbb{P}}newcommand{bs}{boldsymbol}DeclareMathOperator{Gr}{Gr}DeclareMathOperator{im}{im}... Asked on 01/05/2022 0 answer ## Prime ideals of formal power series ring that are above the same prime ideal Let$R$denote a commutative ring with identity and let$R[[X]]$denote thering of formal power series over$R$in an indeterminate$X$. If ... Asked on 01/05/2022 by A. C. Biller 1 answer ## Pull back of a Bounded form Let$(X, omega) $be a complex manifold and let$alpha $be a$p$-form$omega$-bounded on$X$.Let$f:Yto X$be a holomorphic... Asked on 01/05/2022 by Kamel 0 answer ## Set-theoretic generation by circuit polynomials Let$P$be a prime ideal in$S=mathbb{C}[x_1,ldots , x_n],$and write$[n] = { 1, ldots , n }.$The algebraic matroid of$P$can... Asked on 01/05/2022 0 answer ## How to prove that$ sum_{m=0}^{infty} { Gamma{(1+2m)/alpha}over Gamma(1/2+m)} { (-t^2/4)^{m}over m !} ge (alpha/2)^{3}exp(-t^{2}/4) $I would love to prove the following inequality$${1over sqrt{pi} } sum_{m=0}^{infty}Gamma{(1+2m)/alpha}{ (-t^2)^{m}over (2m) !}=$$$$sum_{m=0}^{infty}{ Gamma{(1+2m)/alpha}over Gamma(1/2+m)}{ (-t^2/4)^{m}over m !}... Asked on 01/03/2022 0 answer ## Clarification regarding the definition of absolute height of an algebraic number According to page 1-2 of this paper (https://arxiv.org/abs/0906.4286), Mahler has established the inequality$$|alpha_1 - alpha_2| geq H(alpha_1)^{-(d-1)} tag 1$$to be valid for all... Asked on 01/03/2022 0 answer ## Appearance of proof relevance in "ordinary mathematics?" I've been wondering recently what—if any—applications proof theory has to ordinary mathematics (by which I mean algebra, analysis, topology, and so on). In particular, I'd be fascinated to see a... Asked on 01/03/2022 by mcncm 2 answer ## Reference to a Classical Regularity Theorem (Edited)I need a reference to the following result:If$u in H^2(B_1^+) cap {rm Lip}(B_1^+)\$ satisfiesbegin{cases} {rm div}(F(x,u,nabla u)) = F_0(x,u,nabla u) quad &...

Asked on 01/03/2022 by artful_dodger