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Let $E$ be an elliptic curve given in long Weierstraß form with all coefficients $a_1,a_2,a_3,a_4,a_6 in mathbb{Z}$. It is known that the rational points $E(mathbb{Q})$ form a...
Asked on 11/12/2021 by user6671
1 answerI am working in a setting of set theory where set theory is embedded in simply-typed higher-order logic, basically as described for example inChad E. Brown and Cezary Kaliszyk and...
Asked on 11/12/2021 by Steven Obua
1 answerIs there a closed form for the integral $$int_0^{pi/2}(P_nu^mu(costheta))^2,mathrm dtheta,quadmu>nugt-frac12$$ where $P_nu^mu(x)$ is the associated Legendre function of the first kind?I encountered this integral while...
Asked on 11/12/2021 by 西島晃彦 a.k.a. Teru-san
1 answerLet $k$ be a field and $A$ a commutative $k$-algebra. What are sufficient conditions for the module of derivations $mathrm{Der}_k(A)$ to be finitely generated projective? I'm...
Asked on 11/12/2021 by Tobias Fritz
1 answerThe Lie derivative of a general covariant $4$-tensor is given by$$mathcal{L}_{K}R_{abcd} = X^{e}nabla_{e}R_{abcd} + R_{ebcd}nabla_{a}X^{e} + R_{aecd}nabla_{b}X^{e} + R_{abed}nabla_{c}X^{e} + R_{abce}nabla_{d}X^{e},$$ where $X^{a}$ is a...
Asked on 11/12/2021 by Spoilt Milk
1 answerFor each $x in mathbf{Z}$ let $(eta_t(x))_{tgeq0}$ denote independent copies of a process $(eta_t(0))_{tgeq0}$ defined as follows. The process $eta_t(0)$ takes values in ${-1,1}$, where...
Asked on 11/12/2021
0 answerI'm very new to the Langlands program and I was going through the Gauss reciprocity law, Hilbert's 9th problem, Artin's reciprocity law which allowed him to identify the Artin's L-functions...
Asked on 11/12/2021
0 answerA theorem of Fontaine says that if a geometrically connected smooth proper variety $X$ over $mathbb{Q}$ has good reduction everywhere then $h^{i, j}(X)=0$ for $ineq j$,...
Asked on 11/12/2021
1 answerI have the following function $$int_{-infty}^{infty} left{{2^{1/beta-1/2} over v}right}^{it}{ Gamma{(it+1)/beta}over Gamma{(it+1)/2} }dt$$ where $1<beta<2$, $v>0$. Need to show it is positive. The inverse Mellin...
Asked on 11/09/2021 by Vova
1 answerConsider a collection of $m$ matrices $A_i$ of size $ntimes n$, and a vector $b$ of size $m$. I want to solve the bilinear system...
Asked on 11/09/2021 by grok
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