All Questions

$\DeclareMathOperator\Sha{Sha}$I calculated the Tate–Shafarevich group $\Sha(E/K)[2]$ of the elliptic curve $E:y^2=x^3+17x$ over $K=\Bbb{Q}(\sqrt{-37})$. I calculated that by hand and I reached the ...

I am currently going through Shimura's paper on half-integer weight modular forms. I would like to understand given a 𝑞-expansion of half-integral weight modular forms of arbitrary level and ...

Is there any implementation available of an algorithm which solves in full generality the $S$-unit equation $x+y=1$ in a number field? It seems that Magma solves $ax+by=c$ but only in the algebraic ...

Does anyone know how to find explicit generators for the unit group of a number field on magma? For example, in sage one could do K. = NumberField(x^3+x^2-2*x-1) UnitGroup(K).gens() and it ...

I have an algebra $A$ over a Noetherian ring and an ideal $I=(x,y)$, where $x,y \in A$. I need to examine whether a polynomial $h \in A$ is a zero divisor in $A/I$ or not. Is there a computer algebra ...

Suppose I have an action of a linear reductive group ($GL(2,\mathbb{C})^2$ in this case) on a complex vector space (of dimension $16$) and I want to compute explicitly the ring of invariants of this ...